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Jun 26, 2018
06/18

by
Jason Gaddis; Kenneth L. Price

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The impetus for this study is the work of Dumas and Rigal on the Jordanian deformation of the ring of coordinate functions on $2\times 2$ matrices. We are also motivated by current interest in birational equivalence of noncommutative rings. Recognizing the construction of the Jordanian matrix algebra as a skew polynomial ring, we construct a family of algebras relative to differential operator rings over a polynomial ring in one variable which are birationally equivalent to the Weyl algebra...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1501.07530

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Jun 27, 2018
06/18

by
Aicha Batoul; Kenza Guenda; T. Aaron Gulliver

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In this paper, we give an important isomorphism between contacyclic codes and cyclic codes over finite principal ideal rings. Necessary and sufficient conditions for the existence of non-trivial cyclic self-dual codes over finite principal ideal rings are given.

Topics: Information Theory, Computing Research Repository, Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1505.00876

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Jun 27, 2018
06/18

by
Mohamed Elhamdadi; El-kaïoum M. Moutuou

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We give a foundational account on topological racks and quandles. Specifically, we define the notions of ideals, kernels, units, and inner automorphism group in the context of topological racks. Further, we investigate topological rack modules and principal rack bundles. Central extensions of topological racks are then introduced providing a first step towards a general continuous cohomology theory for topological racks and quandles.

Topics: Quantum Algebra, Mathematics, Algebraic Topology, Rings and Algebras, Geometric Topology

Source: http://arxiv.org/abs/1506.00084

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Jun 28, 2018
06/18

by
Abdenacer Makhlouf

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The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and quantization of $n$-Lie algebras.

Topics: Mathematics, Rings and Algebras, Quantum Algebra

Source: http://arxiv.org/abs/1506.06306

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Jun 28, 2018
06/18

by
Vladimir Dzhunushaliev

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Nonassociative generalization of supersymmetry is suggested. 3- and 4-point associators for supersymmetric generators are considered. On the basis of zero Jacobiators for three supersymmetric generators, we have obtained the simplest form of 3-point associators. The connection between 3- and 4-point associators is considered. On the basis of this connection, 4-point associators are obtained. The Jacobiators for the product of four supersymmetric generators are calculated. We discuss the...

Topics: Mathematical Physics, Mathematics, Rings and Algebras, High Energy Physics - Theory

Source: http://arxiv.org/abs/1509.04614

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4.0

Jun 29, 2018
06/18

by
Mojtaba Sedaghatjoo; Ahmad Khaksari

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In this paper we prove that for a monoid $S$, products of indecomposable right $S$-acts are indecomposable if and only if $S$ contains a right zero. Besides, we prove that subacts of indecomposable right $S$-acts are indecomposable if and only if $S$ is left reversible. Ultimately, we prove that the one element right $S$-act $\Theta_S$ is product flat if and only if $S$ contains a left zero.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1607.00906

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Jun 29, 2018
06/18

by
Shiquan Ruan; Haicheng Zhang

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Let $\A$ be a finitary hereditary abelian category and $D(\A)$ be its reduced Drinfeld double Hall algebra. By giving explicit formulas in $D(\A)$ for left and right mutations, we show that the subalgebras of $D(\A)$ generated by exceptional sequences are invariant under mutation equivalences. As an application, we obtain that if $\A$ is the category of finite dimensional modules over a finite dimensional hereditary algebra, or the category of coherent sheaves on a weighted projective line, the...

Topics: Rings and Algebras, Representation Theory, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1612.09051

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Jun 30, 2018
06/18

by
Birge Huisgen-Zimmermann

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It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the points of which correspond in a natural fashion to the isomorphism types of uniserial left $\Lambda$-modules, and the geometry of which faithfully reflects the constraints met in constructing such modules. A constructive coordinatized access to these varieties...

Topics: Mathematics, Rings and Algebras, Representation Theory

Source: http://arxiv.org/abs/1407.2384

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Jun 30, 2018
06/18

by
J. M. Casas; E. Khmaladze; N. Pacheco Rego

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Non-abelian tensor product of Hom-Lie algebras is constructed and studied. This tensor product is used to describe universal ($\alpha$-)central extensions of Hom-Lie algebras and to establish a relation between cyclic and Milnor cyclic homologies of Hom-associative algebras satisfying certain additional condition.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1409.1729

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Jun 29, 2018
06/18

by
J. Y. Abuhlail; S. N. Il'in; Y. Katsov; T. G. Nam

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In this paper, we introduce and study e-injective semimodules, in particular over additively idempotent semirings. We completely characterize semirings all of whose semimodules are e-injective, describe semirings all of whose projective semimodules are e-injective, and characterize one-sided Noetherian rings in terms of direct sums of e-injective semimodules. Also, we give complete characterizations of bounded distributive lattices, subtractive semirings, and simple semirings, all of whose...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1608.02837

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Jun 30, 2018
06/18

by
Ivana Jovovic; Branko Malesevic

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We consider partial and total reduction of a nonhomogeneous linear system of the operator equations with the system matrix in the same particular form as in paper [N. Shayanfar, M. Hadizadeh 2013]. Here we present two different concepts. One is concerned with partially reduced systems obtained by using the Jordan and the rational form of the system matrix. The other one is dealing with totally reduced systems obtained by finding the adjugate matrix of the characteristic matrix of the system...

Topics: Mathematics, Spectral Theory, Numerical Analysis, Rings and Algebras, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1404.0671

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Jun 27, 2018
06/18

by
Adam Chapman

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We show that if two division $p$-algebras of prime degree share an inseparable field extension of the center then they also share a cyclic separable one. We show that the converse is in general not true. We also point out that sharing all the inseparable field extensions of the center does not imply sharing all the cyclic separable ones.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1503.02342

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Jun 27, 2018
06/18

by
Tudor-Dan Rad; Hans-Peter Schröcker

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We characterise the kinematic image of the constraint variety of a 2R dyad as a regular ruled quadric in a 3-space that contains a "null quadrilateral". Three prescribed poses determine, in general, two such quadrics. This allows us to modify a recent algorithm for the synthesis of 6R linkages in such a way that two consecutive revolute axes coincide, thus producing a 5R linkage. Using the classical geometry of twisted cubics on a quadric, we explain some of the peculiar properties of...

Topics: Robotics, Computing Research Repository, Rings and Algebras, Mathematics, Metric Geometry

Source: http://arxiv.org/abs/1503.04566

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Jun 27, 2018
06/18

by
Bogdan Nica

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Motivated in part by combinatorial applications to certain sum-product phenomena, we introduce unimodular graphs over finite fields and, more generally, over finite valuation rings. We compute the spectrum of the unimodular graphs, by using Eisenstein sums associated to unramified extensions of such rings. We derive an estimate for the number of solutions to the restricted dot product equation $a\cdot b=r$ over a finite valuation ring. Furthermore, our spectral analysis leads to the exact value...

Topics: Combinatorics, Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1505.05034

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Jun 27, 2018
06/18

by
Lucas Calixto; Joel Lemay; Alistair Savage

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We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$, $n \ge 2$. Under some mild assumptions, we prove universality, finite-dimensionality, and tensor product decomposition properties for these modules. These properties are analogues of those of Weyl modules in the non-super setting. We also point out some...

Topics: Mathematics, Rings and Algebras, Representation Theory

Source: http://arxiv.org/abs/1505.06949

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Jun 28, 2018
06/18

by
Julio Benitez; Enrico Boasso

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In this article several properties of the inverse along an element will be studied in the context of unitary rings. New characterizations of the existence of this inverse will be proved. Moreover, the set of all invertible elements along a fixed element will be fully described. Futhermore, commuting inverse along an element will be characterized. The special cases of the group inverse, the (generalized) Drazin inverse and the Moore-Penrose inverse (in rings with involutions) will be also...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1507.05410

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Jun 28, 2018
06/18

by
Gary F. Birkenmeier; C. Edward Ryan

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In this paper we show that for a given set of pairwise comaximal ideals $\{X_i\}_{i\in I}$ in a ring $R$ with unity and any right $R$-module $M$ with generating set $Y$ and $C(X_i)=\sum\limits_{k\in\mathbb{N}}\underline{\ell}_M(X_i^{k})$, $M=\oplus_{i\in I}C(X_i)$ if and only if for every $y\in Y$ there exists a nonempty finite subset $J\subseteq I$ and positive integers $k_j$ such that $\bigcap\limits_{j\in J}X_i^{k_j}\subseteq\underline{r}_R(yR)$. We investigate this decomposition for a...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1508.01543

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Jun 29, 2018
06/18

by
Alina Iacob

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We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the connection between the Gorenstein injective modules and the strongly cotorsion modules. We prove that when the ring R is commutative noetherian of finite Krull dimension, the class of Gorenstein injective modules coincides with that of strongly...

Topics: Commutative Algebra, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1601.04665

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Jun 29, 2018
06/18

by
Marco A. Farinati; A. Patricia Jancsa

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We generalize a result on the Heisenberg Lie algebra that gives restrictions to possible Lie bialgebra cobrackets on 2-step nilpotent algebras with some additional properties. For the class of 2-step nilpotent Lie algebras coming from graphs, we describe these extra properties in a very easy graph-combinatorial way. We exhibit applications for $\mathfrak f_n$, the free 2-step nilpotent Lie algebra.

Topics: Rings and Algebras, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1607.00300

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Jun 29, 2018
06/18

by
Thomas Gobet

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We introduce bijections between generalized type $A_n$ noncrossing partitions (that is, associated to arbitrary standard Coxeter elements) and fully commutative elements of the same type. The latter index the diagram basis of the classical Temperley-Lieb algebra, while for each choice of standard Coxeter element the corresponding noncrossing partitions also index a basis, given by the images in the Temperley-Lieb algebra of the simple elements of the dual Garside structure (associated to this...

Topics: Combinatorics, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1608.04530

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Jun 29, 2018
06/18

by
Dilber Kocak

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For any integer $d\geq 1$ we construct examples of finitely presented algebras with intermediate growth of type $[e^{n^{d/(d+1)}}]$. We produce these examples by computing the growth types of some finitely presented metabelian Lie algebras.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1609.06901

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Jun 29, 2018
06/18

by
F. Y. Yasumura; E. E. A. Hitomi

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Motivated by the combinatorial properties of products in Lie algebras, we investigate the subset of permutations that naturally appears when we write the long commutator [x_1, x_2, ..., x_m] as a sum of associative monomials. We characterize this subset and find some useful equivalences. Moreover, we explore properties concerning the action of this subset on sequences of m elements. In particular we describe sequences that share some special symmetries which can be useful in the study of...

Topics: Combinatorics, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1609.09407

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63

Jun 30, 2018
06/18

by
Cris Negron

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Stefan and Guichardet have provided Lyndon-Hochschild-Serre type spectral sequences which converge to the Hochschild cohomology and Ext groups of a smash product. We show that these spectral sequences carry natural multiplicative structures, and that these multiplicative structures can be used to calculate the cup product on Hochschild cohomology and the Yoneda product on an Ext algebra.

Topics: Mathematics, Quantum Algebra, Rings and Algebras, K-Theory and Homology

Source: http://arxiv.org/abs/1401.3551

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27

Jun 30, 2018
06/18

by
Hebing Rui; Yucai Su

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In this paper, a notion of cyclotomic (or level $k$) walled Brauer algebras $\mathscr B_{k, r, t}$ is introduced for arbitrary positive integer $k$. It is proven that $\mathscr B_{k, r, t}$ is free over a commutative ring with rank $k^{r+t}(r+t)!$ if and only if it is admissible. Using super Schur-Weyl duality between general linear Lie superalgebras $\mathfrak{gl}_{m|n}$ and $\mathscr B_{2, r, t}$, we give a classification of highest weight vectors of $\mathfrak{gl}_{m|n}$-modules...

Topics: Quantum Algebra, Mathematics, Rings and Algebras, Representation Theory

Source: http://arxiv.org/abs/1402.1221

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Jun 30, 2018
06/18

by
Hendrik Lenstra

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The "unit theorem" to which the present mini-course is devoted is a theorem from algebra that has a combinatorial flavour, and that originated in fact from algebraic combinatorics. Beyond a proof, the course also addresses applications, one of which is a proof of the normal basis theorem from Galois theory.

Topics: Rings and Algebras, Combinatorics, Mathematics

Source: http://arxiv.org/abs/1703.07273

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Jun 27, 2018
06/18

by
Robert Laugwitz

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In this paper, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf algebras which are of what we call weakly separable type over a group, we obtain a class of pointed Hopf algebras which can be viewed as natural generalizations of multiparameter deformations of universal enveloping algebras of Lie algebras. These Hopf algebras are instances of a new version of braided Drinfeld doubles,...

Topics: Rings and Algebras, Mathematics, Quantum Algebra, Representation Theory

Source: http://arxiv.org/abs/1504.06456

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Jun 28, 2018
06/18

by
Markus Linckelmann

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Using that integrable derivations of symmetric algebras can be interpreted in terms of Bockstein homomorphisms in Hochschild cohomology, we show that integrable derivations are invariant under the transfer maps in Hochschild cohomology of symmetric algebras induced by stable equivalences of Morita type. With applications in block theory in mind, we allow complete discrete valuation rings of unequal characteristic.

Topics: Mathematics, Rings and Algebras, Representation Theory

Source: http://arxiv.org/abs/1506.04676

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6.0

Jun 28, 2018
06/18

by
Pudji Astuti; Harald K. Wimmer

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A subspace $X$ of a vector space over a field $K$ is hyperinvariant with respect to an endomorphism $f$ of $V$ if it is invariant for all endomorphisms of $V$ that commute with $f$. We assume that $f$ is locally nilpotent, that is, every $ x \in V $ is annihilated by some power of $f$, and that $V$ is an infinite direct sum of $f$-cyclic subspaces. In this note we describe the lattice of hyperinvariant subspaces of $V$. We extend results of Fillmore, Herrero and Longstaff (Linear Algebra Appl....

Topics: Functional Analysis, Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1511.07771

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Jun 30, 2018
06/18

by
Juan Cuadra; Pavel Etingof; Chelsea Walton

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We study actions of semisimple Hopf algebras H on Weyl algebras A over a field of characteristic zero. We show that the action of H on A must factor through a group algebra; in other words, if H acts inner faithfully on A, then H is cocommutative. The techniques used include reduction modulo a prime number and the study of semisimple cosemisimple Hopf actions on division algebras.

Topics: Mathematics, Quantum Algebra, Rings and Algebras

Source: http://arxiv.org/abs/1409.1644

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Jun 30, 2018
06/18

by
Kevin Coulembier; Ian M. Musson

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We study inclusions between primitive ideals in the universal enveloping algebra of general linear superalgebras. For classical Lie superalgebras, any primitive ideal is the annihilator of a simple highest weight module. It therefore suffices to study the quasi-order on highest weights determined by the relation of inclusion between primitive ideals. For the specific case of reductive Lie algebras, this quasi-order is essentially the left Kazhdan-Lusztig quasi-order. For Lie superalgebras, the...

Topics: Mathematics, Rings and Algebras, Representation Theory

Source: http://arxiv.org/abs/1409.2532

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Jun 26, 2018
06/18

by
Florin Panaite; Freddy Van Oystaeyen

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We define the concept of weak pseudotwistor for an algebra $(A, \mu)$ in a monoidal category $\mathcal{C}$, as a morphism $T:A\otimes A\rightarrow A\otimes A$ in $\mathcal{C}$, satisfying some axioms ensuring that $(A, \mu \circ T)$ is also an algebra in $\mathcal{C}$. This concept generalizes the previous proposal called pseudotwistor and covers a number of exemples of twisted algebras that cannot be covered by pseudotwistors, mainly examples provided by Rota-Baxter operators and some of their...

Topics: Mathematics, Rings and Algebras, Quantum Algebra

Source: http://arxiv.org/abs/1502.05327

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58

Jun 30, 2018
06/18

by
Adam Chapman

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We discuss the Kummer subspaces of tensor products of cyclic algebras, focusing mainly on the case of cyclic algebras of degree 3. We present a family of maximal spaces in the general case, classify all the monomial spaces in the case of tensor products of cyclic algebras of degree 3 using graph theory, and provide an upper bound for the dimension in the generic tensor product of cyclic algebras of degree 3.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1405.0188

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Jun 29, 2018
06/18

by
Jiefeng Liu; Abdenacer Makhlouf; Yunhe Sheng

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In this paper, we introduce the notion of generalized representation of a $3$-Lie algebra, by which we obtain a generalized semidirect product $3$-Lie algebra. Moreover, we develop the corresponding cohomology theory. Various examples of generalized representations of 3-Lie algebras and computation of 2-cocycles of the new cohomology are provided. Also, we show that a split abelian extension of a 3-Lie algebra is isomorphic to a generalized semidirect product $3$-Lie algebra. Furthermore, we...

Topics: Representation Theory, Mathematical Physics, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1609.01549

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Jun 30, 2018
06/18

by
Dieter Happel; Birge Huisgen-Zimmermann

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We develop criteria for deciding the contravariant finiteness status of a subcategory $A \subseteq \Lambda\text{-mod}$, where $\Lambda$ is a finite dimensional algebra. In particular, given a finite dimensional $\Lambda$-module $X$, we introduce a certain class of modules -- we call them $A$-phantoms of $X$ -- which indicate whether or not $X$ has a right $A$-approximation: We prove that $X$ fails to have such an approximation if and only if $X$ has infinite-dimensional $A$-phantoms. Moreover,...

Topics: Mathematics, Rings and Algebras, Representation Theory

Source: http://arxiv.org/abs/1407.2327

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Jun 28, 2018
06/18

by
Donatien Gaparayi; A. Nourou Issa

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A Hom-Lie-Yamaguti algebra, whose ternary operation expresses through its binary one in a specific way, is a multiplicative Hom-Malcev algebra. Any multiplicative Hom-Malcev algebra over a field of characteristic zero has a natural Hom-Lie-Yamaguti structure.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1507.01691

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Jun 28, 2018
06/18

by
Nabilah Abughazalah; Pavel Etingof

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We give an accessible introduction into the theory of lower central series of associative algebras, exhibiting the interplay between algebra, geometry and representation theory that is characteristic for this subject, and to discuss some open questions. In particular, we provide shorter and clearer proofs of the main results of this theory. We also discuss some new theoretical and computational results and conjectures on the lower central series of the free algebra in two generators modulo a...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1508.00943

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10.0

Jun 28, 2018
06/18

by
Andrew Misseldine

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Any Schur ring is uniquely determined by a partition of the elements of the group. An open question in the study of Schur rings is determining which partitions of the group induce a Schur ring. Although a structure theorem is available for Schur rings over cyclic groups, it is still a difficult problem to count all the partitions. For example, Kovacs, Liskovets, and Poschel determine formulas to count the number of wreath-indecomposable Schur rings. In this paper we solve the problem of...

Topics: Group Theory, Mathematics, Rings and Algebras, Representation Theory

Source: http://arxiv.org/abs/1508.03757

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Jun 30, 2018
06/18

by
Daniel Berlyne

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This paper is a translation of the paper "Idealtheorie in Ringbereichen", written by Emmy Noether in 1920, from the original German into English. It in particular brings the language used into the modern world so that it is easily understandable by the mathematicians of today. The paper itself deals with ideal theory, and was revolutionary in its field, that is modern algebra. Topics covered include: the representation of an ideal as the least common multiple of irreducible ideals;...

Topics: Mathematics, Rings and Algebras, Commutative Algebra

Source: http://arxiv.org/abs/1401.2577

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Jun 30, 2018
06/18

by
Eliezer Batista; Joost Vercruysse

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The duality between partial actions (partial $H$-module algebras) and co-actions (partial $H$-comodule algebras) of a Hopf algebra $H$ is fully explored in this work. A connection between partial (co)actions and Hopf algebroids is established under certain commutativity conditions. Moreover, we continue this duality study, introducing also partial $H$-module coalgebras and their associated $C$-rings, partial $H$-comodule coalgebras and their associated cosmash coproducts, as well as the mutual...

Topics: Mathematics, Quantum Algebra, Rings and Algebras

Source: http://arxiv.org/abs/1403.1399

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Jun 30, 2018
06/18

by
Ted Chinburg; Holley Friedlander; Sean Howe; Michiel Kosters; Bhairav Singh; Matthew Stover; Ying Zhang; Paul Ziegler

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The purpose of this paper is to give presentations for projective $S$-unit groups of the Hurwitz order in Hamilton's quaternions over the rational field $\mathbb{Q}$. To our knowledge, this provides the first explicit presentations of an $S$-arithmetic lattice in a semisimple Lie group with $S$ large. In particular, we give presentations for groups acting irreducibly and cocompactly on a product of Bruhat--Tits trees. We also include some discussion and experimentation related to the congruence...

Topics: Geometric Topology, Mathematics, Rings and Algebras, Number Theory, Group Theory

Source: http://arxiv.org/abs/1404.6091

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Jun 30, 2018
06/18

by
Pedro A. Guil Asensio; Ashish K. Srivastava

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A module is called automorphism-invariant if it is invariant under any automorphism of its injective envelope. In this survey article we present the current state of art dealing with such class of modules.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1405.1051

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Jun 30, 2018
06/18

by
Galina Deryabina; Alexei Krasilnikov

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Let $F$ be a field and let $F \langle X \rangle$ be the free unital associative $F$-algebra on the free generating set $X = \{ x_1, x_2, \dots \}$. A subalgebra (a vector subspace) $V$ in $F \langle X \rangle$ is called a $T$-subalgebra (a $T$-subspace) if $\phi (V) \subseteq V$ for all endomorphisms $\phi$ of $F \langle X \rangle$. For an algebra $G$, its central polynomials form a $T$-subalgebra $C(G)$ in $F \langle X \rangle$. Over a field of characteristic $p > 2$ there are algebras $G$...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1409.7937

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Jun 30, 2018
06/18

by
Jonas Deré

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In this paper, we study positive as well as non-negative and non-trivial gradings on finite dimensional Lie algebras. We give a different proof that the existence of such a grading on a Lie algebra is invariant under taking field extensions, a result very recently obtained by Y. Cornulier. Similarly, we prove that given a grading of one these types and a finite group of automorphisms, there always exist a positive grading which is preserved by this group. From these results we conclude that the...

Topics: Mathematics, Rings and Algebras, Dynamical Systems

Source: http://arxiv.org/abs/1410.3713

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Jun 25, 2018
06/18

by
Gerhard Wendt

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We give a classification of $1$-primitive near-rings using sandwich centralizer near-rings

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1501.01842

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73

Jun 27, 2018
06/18

by
Laiachi El Kaoutit; José Gómez-Torrecillas

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We recognise Harada's generalized categories of diagrams as a particular case of modules over a monad defined on a finite direct product of additive categories. We work in the dual (albeit formally equivalent) situation, that is, with comodules over comonads. With this conceptual tool at hand, we obtain several of the Harada results with simpler proofs, some of them under more general hypothesis, besides with a characterization of the normal triangular matrix comonads that are hereditary, that...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1504.07594

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86

Jun 29, 2018
06/18

by
Jerzy Matczuk

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Question 3 of [3] asks whether the matrix ring Mn(R) is nil clean, for any nil clean ring R. It is shown that positive answer to this question is equivalent to positive solution for Kothe's problem in the class of algebras over the field F_2. Other equivalent problems are also discussed. The classes of conjugate clean and conjugate nil clean rings, which lie strictly between uniquely (nil) clean and (nil) clean rings are introduced and investigated.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1605.09534

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206

Jun 30, 2018
06/18

by
Alessandro De Paris

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To our knowledge at the time of writing, the maximum Waring rank for the set of all ternary forms of degree $d$ (with coefficients in an algebraically closed field of characteristic zero) is known only for $d\le 4$. The best upper bound that is known for $d=5$ is twelve, and in this work we lower it to ten.

Topics: Mathematics, Rings and Algebras, Commutative Algebra, Algebraic Geometry

Source: http://arxiv.org/abs/1409.7643

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95

Jun 27, 2018
06/18

by
Houyi Yu

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Rota-Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial algebra $\mathbf{k}[x]$ plays a central role both in analysis and algebra. In this paper, we explicitly classified all monomial Rota-Baxter operators on $\mathbf{k}[x]$.

Topics: Commutative Algebra, Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1503.02606

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172

Jun 27, 2018
06/18

by
Naihuan Jing; Jian Zhang

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Quantum determinants and Pfaffians or permanents and Hafnians are introduced on the two parameter quantum general linear group. Fundamental identities among quantum Pf, Hf, and det are proved in the general setting. We show that there are two special quantum algebras among the quantum groups, where the quantum Pfaffians have integral Laurent polynomials as coefficients. As a consequence, the quantum Hafnian is computed by a closely related quantum permanent and identical to the quantum Pfaffian...

Topics: Combinatorics, Rings and Algebras, Mathematics, Quantum Algebra, Mathematical Physics

Source: http://arxiv.org/abs/1504.01538

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16

Jun 27, 2018
06/18

by
Henning Krause

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We provide several equivalent descriptions of a highest weight category using recollements of abelian categories. Also, we explain the connection between sequences of standard and exceptional objects.

Topics: Mathematics, Rings and Algebras, Representation Theory, Algebraic Geometry

Source: http://arxiv.org/abs/1506.01485