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4.0

Apr 26, 2017
04/17

Apr 26, 2017
by
Hongxing Wang; Jianlong Chen

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In this paper, we introduce a weak group inverse (called the WG inverse in the present paper) for square matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and derive several characterizations of the two orders. At last, one characterization of the core-EP order is derived by using the WG inverses.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.08403

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3.0

Apr 26, 2017
04/17

Apr 26, 2017
by
Yin Chen; Ziping Zhang; Runxuan Zhang; Rushu Zhuang

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Let $(\mathfrak{g},\omega)$ be a finite-dimensional non-Lie complex $\omega$-Lie algebra. We study the derivation algebra $Der(\mathfrak{g})$ and the automorphism group $Aut(\mathfrak{g})$ of $(\mathfrak{g},\omega)$. We introduce the notions of $\omega$-derivations and $\omega$-automorphisms of $(\mathfrak{g},\omega)$ which naturally preserve the bilinear form $\omega$. We show that the set $Der_{\omega}(\mathfrak{g})$ of all $\omega$-derivations is a Lie subalgebra of $Der(\mathfrak{g})$ and...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.08042

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3.0

Apr 26, 2017
04/17

Apr 26, 2017
by
Askar Tuganbaev

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Every automorphism-invariant right non-singular $A$-module is injective if and only if the factor ring of the ring $A$ with respect to its right Goldie radical is a right strongly semiprime ring.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.08341

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3.0

Apr 26, 2017
04/17

Apr 26, 2017
by
Jordan Courtemanche; Manfred Dugas; Daniel Herden

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Let $R$ be a commutative, indecomposable ring with identity and $(P,\le)$ a partially ordered set. Let $FI(P)$ denote the finitary incidence algebra of $(P,\le)$ over $R$. We will show that, in most cases, local automorphisms of $FI(P)$ are actually $R$-algebra automorphisms. In fact, the existence of local automorphisms which fail to be $R$-algebra automorphisms will depend on the chosen model of set theory and will require the existence of measurable cardinals. We will discuss local...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.08365

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Apr 25, 2017
04/17

Apr 25, 2017
by
Peigen Cao; Min Huang; Fang Li

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Using the unfolding method given in \cite{HL}, we prove the conjectures on sign-coherence and a recurrence formula respectively of ${\bf g}$-vectors for acyclic sign-skew-symmetric cluster algebras. As a following consequence, the conjecture is affirmed in the same case which states that the ${\bf g}$-vectors of any cluster form a basis of $\mathbb Z^n$. Also, the additive categorification of an acyclic sign-skew-symmetric cluster algebra $\mathcal A(\Sigma)$ is given, which is realized as...

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

Source: http://arxiv.org/abs/1704.07549

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Apr 24, 2017
04/17

Apr 24, 2017
by
Alexey Gordienko; Ofir Schnabel

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When one studies the structure (e.g. graded ideals, graded subspaces, radicals, ...) or graded polynomial identities of graded algebras, the grading group itself does not play an important role, but can be replaced by any other group that realizes the same grading. Here we come to the notion of weak equivalence of gradings: two gradings are weakly equivalent if there exists an isomorphism between the graded algebras that maps each graded component onto a graded component. The following question...

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

Source: http://arxiv.org/abs/1704.07170

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6.0

Apr 24, 2017
04/17

Apr 24, 2017
by
Volodymyr Bavula; Vyacheslav Futorny

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Let R be a ring (not necessarily with 1) and G be a finite group of automorphisms of R. The set B(R, G) of primes p such that p | |G| and R is not p-torsion free, is called the set of bad primes. When the ring is |G|-torsion free, i.e., B(R, G) is empty set, the properties of the rings R and R^G are closely connected. The aim of the paper is to show that this is also true when B(R, G) is not empty set under natural conditions on bad primes. In particular, it is shown that the Jacobson radical...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.07190

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3.0

Apr 23, 2017
04/17

Apr 23, 2017
by
Amir Hossein Nokhodkar

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It is shown that an anisotropic orthogonal involution in characteristic two is totally decomposable if it is totally decomposable over a separable extension of the ground field. In particular, this settles a characteristic two analogue of a conjecture formulated by Bayer-Fluckiger et al.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.06887

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4.0

Apr 21, 2017
04/17

Apr 21, 2017
by
Frederik Marks; Jorge Vitória

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An important result in tilting theory states that a class of modules over a ring is a tilting class if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective dimension. Moreover, cotilting classes are precisely the resolving and definable subcategories of the module category whose Ext-orthogonal class has bounded injective dimension. In this article, we prove a derived counterpart of the statements above in the context of silting theory. Silting and...

Topics: Rings and Algebras, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1704.06484

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5.0

Apr 21, 2017
04/17

Apr 21, 2017
by
Silvana Bazzoni; Manuel Cortés Izurdiaga; Sergio Estrada

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We study the behaviour of modules $M$ that fit into a short exact sequence $0\to M\to C\to M\to 0$, where $C$ belongs to a class of modules $\mathcal C$, the so-called $\mathcal C$-periodic modules. We find a rather general framework to improve and generalize some well-known results of Benson and Goodearl and Simson. In the second part we will combine techniques of hereditary cotorsion pairs and presentation of direct limits, to conclude, among other applications, that if $M$ is any module and...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.06672

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3.0

Apr 21, 2017
04/17

Apr 21, 2017
by
Shan Chang

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Let $G$ be a finite group, $\Omega(G)$ be its Burnside ring, and $\Delta(G)$ its augmentation ideal. Denote by $\Delta^n(G)$ and $Q_n(G)$ the $n$-th power of $\Delta(G)$ and the $n$-th consecutive quotient group $\Delta^n(G)/\Delta^{n+1}(G)$, respectively. This paper provides an explicit $\mathbb{Z}$-basis for $\Delta^n(\mathcal{H})$ and determine the isomorphism class of $Q_n(\mathcal{H})$ for each positive integer $n$, where $\mathcal{H}=\langle g,h |\, g^{p^m}=h^p=1,...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.06538

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Apr 21, 2017
04/17

Apr 21, 2017
by
M. C. Iovanov

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We study generalized comatrix coalgebras and upper triangular comatrix coalgebras, which are not only a dualization but also an extension of classical generalized matrix algebras. We use these to answer several questions on Noetherian and Artinian type notions in the theory of coalgebras, and to give complete connections between these. We also solve completely the so called finite splitting problem for coalgebras: we show that a coalgebra $C$ has the property that the rational part of every...

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

Source: http://arxiv.org/abs/1704.06708

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7.0

Apr 20, 2017
04/17

Apr 20, 2017
by
Tom De Medts; Michiel Van Couwenberghe

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We introduce axial representations and modules over axial algebras as new tools to study axial algebras. All known interesting examples of axial algebras fall into this setting, in particular the Griess algebra whose automorphism group is the Monster group. Our results become especially interesting for Matsuo algebras. We vitalize the connection between Matsuo algebras and 3-transposition groups by relating modules over Matsuo algebras with representations of 3-transposition groups. As a...

Topics: Group Theory, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.06111

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6.0

Apr 20, 2017
04/17

Apr 20, 2017
by
David Hernandez

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R-matrices are the solutions of the Yang-Baxter equation. At the origin of the quantum group theory, they may be interpreted as intertwining operators. Recent advances have been made independently in different directions. Maulik-Okounkov have given a geometric approach to R-matrices with new tools in symplectic geometry, the stable envelopes. Kang-Kashiwara-Kim-Oh proved a conjecture on the categorification of cluster algebras by using R-matrices in a crucial way. Eventually, a better...

Topics: Mathematical Physics, Representation Theory, Quantum Algebra, Rings and Algebras, Algebraic...

Source: http://arxiv.org/abs/1704.06039

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10.0

Apr 20, 2017
04/17

Apr 20, 2017
by
Dietrich Burde; Karel Dekimpe; Bert Verbeke

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We study almost inner derivations of Lie algebras, which were introduced by Gordon and Wilson in their work on isospectral deformations of compact solvmanifolds. We compute all almost inner derivations for low-dimensional Lie algebras, and introduce the concept of fixed basis vectors for proving that all almost inner derivations are inner for $2$-step nilpotent Lie algebras determined by graphs, free $2$ and $3$-step nilpotent Lie algebras, free metabelian nilpotent Lie algebras on two...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.06159

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7.0

Apr 20, 2017
04/17

Apr 20, 2017
by
Gunnar Fløystad; Hans Munthe-Kaas

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We relate composition and substitution in pre- and post-Lie algebras to algebraic geometry. The Connes-Kreimer Hopf algebras, and MKW Hopf algebras are then coordinate rings of the infinite-dimensional affine varieties consisting of series of trees, resp.\ Lie series of ordered trees. Furthermore we describe the Hopf algebras which are coordinate rings of the automorphism groups of these varieties, which govern the substitution law in pre- and post-Lie algebras.

Topics: Rings and Algebras, Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1704.06171

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3.0

Apr 19, 2017
04/17

Apr 19, 2017
by
Alexandr Kazda; Matt Valeriote

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In this paper we investigate the computational complexity of deciding if a given finite algebraic structure satisfies a fixed (strong) Maltsev condition $\Sigma$. Our goal in this paper is to show that $\Sigma$-testing can be accomplished in polynomial time when the algebras tested are idempotent and the Maltsev condition $\Sigma$ can be described using paths. Examples of such path conditions are having a Maltsev term, having a majority operation, and having a chain of J\'onsson (or Gumm) terms...

Topics: Rings and Algebras, Computational Complexity, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1704.05928

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4.0

Apr 19, 2017
04/17

Apr 19, 2017
by
Benjamin Briggs

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In this note we discuss an interesting duality known to occur for certain complex reflection groups, we prove in particular that this duality has a concrete representation theoretic realisation. As an application, we construct matrix factorisations of the highest degree basic invariant which give free resolutions of the module of K\"{a}hler differentials of the coinvariant algebra $A$ associated to such a reflection group. From this one can read off the Hilbert series of ${\rm...

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

Source: http://arxiv.org/abs/1704.05966

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4.0

Apr 19, 2017
04/17

Apr 19, 2017
by
Jiafeng Lv; Sei-Qwon Oh; Xingting Wang; Xiaolan Yu

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Certain sufficient homological and ring-theoretical conditions are given for a Hopf algebra to have bijective antipode with applications to noetherian Hopf algebras regarding their homological behaviors.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.05731

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5.0

Apr 18, 2017
04/17

Apr 18, 2017
by
B. Herlemont; O. Ogievetsky

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We construct the rings of generalized differential operators on the $\h$-deformed vector space of $\mathbf{gl}$-type. In contrast to the $q$-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of $\h$-deformed differential operators $\Diffs(n)$ is labeled by a rational function $\sigma$ in $n$ variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some...

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

Source: http://arxiv.org/abs/1704.05330

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4.0

Apr 18, 2017
04/17

Apr 18, 2017
by
Paolo Lipparini

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We present some identities dealing with reflexive and admissible relations and which, through a variety, are equivalent to congruence modularity.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.05274

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4.0

Apr 18, 2017
04/17

Apr 18, 2017
by
Benjamin Antieau; Asher Auel; Colin Ingalls; Daniel Krashen; Max Lieblich

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The standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a $p$-adic field predicts that the index divides the cube of the period. Using Gabber's theory of prime-to-$\ell$ alterations and the deformation theory of twisted sheaves, we prove that the index divides the fourth power of the period for every Brauer class whose period is prime to $6p$, giving the first uniform period-index bounds over such fields.

Topics: Rings and Algebras, Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1704.05489

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4.0

Apr 17, 2017
04/17

Apr 17, 2017
by
Alveri Sant'Ana; Robson Vinciguerra

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In this paper we discuss under which conditions cyclic essential extensions of simple modules over a differential operator ring R[z;d] are Artinian. In particular, we study the case when R is either d-simple or d-primitive. Furthermore, we obtain important results when R is an affine algebra of Kull dimension 2. As an application we characterize the differential operator rings C[x,y][z;d] for which cyclic essential extensions of simple modules are Artinian.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.04970

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5.0

Apr 17, 2017
04/17

Apr 17, 2017
by
U. Bekbaev

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The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by attaching them some quadratic forms.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.05171

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4.0

Apr 17, 2017
04/17

Apr 17, 2017
by
Wei Hu; Changchang Xi

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Derived equivalences for Artin algebras (and almost $\nu$-stable derived equivalences for finite-dimensional algebras) are constructed from Milnor squares of algebras. Particularly, three operations of gluing vertices, unifying arrows and identifying socle elements on derived equivalent algebras are presented to produce new derived equivalences of the resulting algebras from the given ones. As a byproduct, we construct a series of derived equivalences, showing that derived equivalences may...

Topics: Rings and Algebras, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1704.04914

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4.0

Apr 14, 2017
04/17

Apr 14, 2017
by
A. Nyman

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Let $k$ be a field. We describe necessary and sufficient conditions for a $k$-linear abelian category to be a noncommutative $\mathbb{P}^{1}$-bundle over a pair of division rings over $k$. As an application, we prove that $\mathbb{P}^{1}_{n}$, Piontkovski's $n$th noncommutative projective line, is the noncommutative projectivization of an $n$-dimensional vector space.

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

Source: http://arxiv.org/abs/1704.04544

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5.0

Apr 13, 2017
04/17

Apr 13, 2017
by
Jianjun Qiu; Yuqun Chen

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We establish the Gr\"obner-Shirshov bases theory for differential Lie $\Omega$-algebras. As an application, we give a linear basis of a free differential Lie Rota-Baxter algebra on a set.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.04493

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5.0

Apr 13, 2017
04/17

Apr 13, 2017
by
Adam Jacoby

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A classical theorem of I. Schur states that the degree of any irreducible complex representation of a finite group $G$ divides the order of $G/\mathscr{Z} G$, where $\mathscr{Z} G$ is the center $G$. This note discusses similar divisibility results for certain classes of Hopf algebras.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.04256

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4.0

Apr 12, 2017
04/17

Apr 12, 2017
by
Aravind Asok; Marc Hoyois; Matthias Wendt

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We study generically split octonion algebras over schemes using techniques of ${\mathbb A}^1$-homotopy theory. By combining affine representability results with techniques of obstruction theory, we establish classification results over smooth affine schemes of small dimension. In particular, for smooth affine schemes over algebraically closed fields, we show that generically split octonion algebras may be classified by characteristic classes including the second Chern class and another...

Topics: Algebraic Topology, Rings and Algebras, Algebraic Geometry, K-Theory and Homology, Mathematics

Source: http://arxiv.org/abs/1704.03657

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7.0

Apr 12, 2017
04/17

Apr 12, 2017
by
Darij Grinberg; Jia Huang; Victor Reiner

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This paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalizes the critical groups of complex finite group representations studied by Benkart, Klivans, Reiner and Gaetz. A formula is given for the cardinality of the critical group generally, and the critical group for the regular representation is described completely. A key role in the formulas is played by the greatest common divisor of the dimensions of the indecomposable...

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

Source: http://arxiv.org/abs/1704.03778

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8.0

Apr 11, 2017
04/17

Apr 11, 2017
by
A. Melakhessou; K. Guenda; T. A. Gulliver; M. Shi; P. Solé

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In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring $R=\F_{q}+v\F_{q}+v^{2}\F_{q}$, where $v^{3}=v$, for $q$ odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over $R$. Further, we give bounds on the minimum distance of LCD codes over $\F_q$ and extend these to codes over $R$.

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

Source: http://arxiv.org/abs/1704.03519

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4.0

Apr 10, 2017
04/17

Apr 10, 2017
by
Andrés Angel; Diego Duarte

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We study a Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the group ring of finitely generated abelian groups. The Batalin-Vilkovisky algebra structure for finite abelian groups comes from the fact that the group ring of finite groups is a symmetric algebra, and the Batalin-Vilkovisky algebra structure for free abelian groups of finite rank comes from the fact that its group ring is a Calabi-Yau algebra.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.03075

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3.0

Apr 10, 2017
04/17

Apr 10, 2017
by
Wolfram Decker; Christian Eder; Viktor Levandovskyy; Sharwan K. Tiwari

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In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the graded case. In the general case, our algorithm is probabilistic in the sense that the resulting Gr\"obner basis can only be expected to generate the given ideal, with high probability. We have implemented our algorithm in the computer algebra system...

Topics: Rings and Algebras, Symbolic Computation, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1704.02852

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4.0

Apr 9, 2017
04/17

Apr 9, 2017
by
Tobias Rossmann

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Let $\mathfrak{O}$ be a compact discrete valuation ring of characteristic zero. Given a module $M$ of matrices over $\mathfrak{O}$, we study the generating function encoding the average sizes of the kernels of the elements of $M$ over finite quotients of $\mathfrak{O}$. We prove rationality and establish fundamental properties of these generating functions and determine them explicitly for various natural families of modules $M$. Using $p$-adic Lie theory, we then show that special cases of...

Topics: Group Theory, Rings and Algebras, Number Theory, Combinatorics, Mathematics

Source: http://arxiv.org/abs/1704.02668

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4.0

Apr 8, 2017
04/17

Apr 8, 2017
by
John Eggers; Ron Evans; Mark Van Veen

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Let $M_n(K)$ denote the algebra of $n \times n$ matrices over a field $K$ of characteristic zero. A nonunital subalgebra $N \subset M_n(K)$ will be called a nonunital intersection if $N$ is the intersection of two unital subalgebras of $M_n(K)$. Appealing to recent work of Agore, we show that for $n \ge 3$, the dimension (over $K$) of a nonunital intersection is at most $(n-1)(n-2)$, and we completely classify the nonunital intersections of maximum dimension $(n-1)(n-2)$. We also classify the...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.02437

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Apr 8, 2017
04/17

Apr 8, 2017
by
Tiwei Zhao

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In this paper, we define a class of relative derived functors in terms of left or right weak flat resolutions to compute the weak flat dimension of modules. Moreover, we investigate two classes of modules larger than that of weak injective and weak flat modules, study the existence of covers and preenvelopes, and give some applications.

Topics: Rings and Algebras, Category Theory, Mathematics

Source: http://arxiv.org/abs/1704.02456

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4.0

Apr 7, 2017
04/17

Apr 7, 2017
by
Alexander Sakhnovich

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The results on the inversion of convolution operators and Toeplitz matrices in the 1-D (one dimensional) case are classical and have numerous applications. We consider a 2-D case of Toeplitz-block Toeplitz matrices, describe a minimal information, which is necessary to recover the inverse matrices, and give a complete characterisation of the inverse matrices.

Topics: Classical Analysis and ODEs, Rings and Algebras, Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1704.02267

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6.0

Apr 6, 2017
04/17

Apr 6, 2017
by
Jin Cao

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We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential graded modules over such an algebra, we also provide a criterion for the existence of a t-structure on the derived category together with a characterization of the coordinate ring of the Tannakian fundamental group of its heart.

Topics: Rings and Algebras, Category Theory, Mathematics

Source: http://arxiv.org/abs/1704.01734

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4.0

Apr 5, 2017
04/17

Apr 5, 2017
by
Simion Breaz; Andrada Cî mpean

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We study the class of rings $R$ with the property that for $x\in R$ at least one of the elements $x$ and $1+x$ are tripotent.

Topics: Rings and Algebras, Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1704.01303

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4.0

Apr 5, 2017
04/17

Apr 5, 2017
by
Mengtian Guo; Xianguo Hu; Jiafeng Lu; Xingting Wang

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In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of Poisson Hopf algebras in the differential graded setting. The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras are discussed.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.01322

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4.0

Apr 5, 2017
04/17

Apr 5, 2017
by
Xianguo Hu; Jiafeng Lu; Xingting Wang

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For any differential graded (DG for short) Poisson algebra $A$ given by generators and relations, we give a "formula" for computing the universal enveloping algebra $A^e$ of $A$. Moreover, we prove that $A^e$ has a Poincar\'e-Birkhoff-Witt basis provided that $A$ is a graded commutative polynomial algebra. As an application of the PBW-basis, we show that a DG symplectic ideal of a DG Poisson algebra $A$ is the annihilator of a simple DG Poisson $A$-module, where $A$ is the DG Poisson...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.01319

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Apr 5, 2017
04/17

Apr 5, 2017
by
Hop D. Nguyen

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Absolutely Koszul algebras are a class of rings over which any finite graded module has a rational Poincar\'e series. We provide a criterion to detect non-absolutely Koszul rings. Combining the criterion with machine computations, we identify large families of Veronese subrings and Segre products of polynomial rings which are not absolutely Koszul. In particular, we classify completely the absolutely Koszul algebras among Segre products of polynomial rings, at least in characteristic $0$.

Topics: Rings and Algebras, Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1704.01654

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3.0

Apr 4, 2017
04/17

Apr 4, 2017
by
G. -S. Zhou; Y. Shen; D. -M. Lu

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We show that a noetherian ring graded by an abelian group of finite rank satisfies the Auslander condition if and only if it satisfies the graded Auslander condition. In addition, we also study the injective dimension, the global dimension and the Cohen-Macaulay property from the same perspective of that for the Auslander condtion. A key step of our approach is to establish homological relations between a graded ring $R$, its quotient ring modulo the ideal $\hbar R$ and its localization ring...

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

Source: http://arxiv.org/abs/1704.00987

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5.0

Apr 4, 2017
04/17

Apr 4, 2017
by
Pere Ara; Roozbeh Hazrat; Huanhuan Li; Aidan Sims

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We study the category of left unital graded modules over the Steinberg algebra of a graded ample Hausdorff groupoid. In the first part of the paper, we show that this category is isomorphic to the category of unital left modules over the Steinberg algebra of the skew-product groupoid arising from the grading. To do this, we show that the Steinberg algebra of the skew product is graded isomorphic to a natural generalisation of the the Cohen-Montgomery smash product of the Steinberg algebra of...

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

Source: http://arxiv.org/abs/1704.01214

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3.0

Apr 3, 2017
04/17

Apr 3, 2017
by
Cristina Flaut

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In this paper we improve the level and sublevel of algebras obtained by the Cayley-Dickson process when their level and sublevel are greater than dimension of the algebras.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.00772

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5.0

Apr 3, 2017
04/17

Apr 3, 2017
by
Darij Grinberg

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Fix a commutative ring $\mathbf{k}$, an element $\beta\in \mathbf{k}$ and an integer $n>0$. Let $\mathcal{X}$ be the polynomial ring over $\mathbf{k}$ in the $n(n-1)/2$ indeterminates $x_{i,j}$ for all $1\leq i

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

Source: http://arxiv.org/abs/1704.00839

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4.0

Apr 2, 2017
04/17

Apr 2, 2017
by
Qunhua Liu; Dong Yang

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We construct a matrix algebra $\Lambda(A,B)$ from two given finite dimensional elementary algebras $A$ and $B$ and give some sufficient conditions on $A$ and $B$ under which the derived Jordan--H\"older property (DJHP) fails for $\Lambda(A,B)$. This provides finite dimensional algebras of finite global dimension which do not satisfy DJHP.

Topics: Rings and Algebras, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1704.00398

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3.0

Apr 1, 2017
04/17

Apr 1, 2017
by
Huanyin Chen; Marjan Sheibani Abdolyousefi

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A ring R is Yaqub nil-clean if for any a\in R, a-a^3 or a+a^3 is nilpotent for all a\in R. We prove that a ring R is Yaqub nil-clean if and only if for any a\in R, there exists some e^3=e\in R, such that a-e or a+3e is nilpotent and ae=ea.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.00213

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4.0

Apr 1, 2017
04/17

Apr 1, 2017
by
Xianhui Fu; Ivo Herzog

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Let $R$ be an associative ring with unit and denote by $K({\rm R \mbox{-}Proj})$ the homotopy category of complexes of projective left $R$-modules. Neeman proved the theorem that $K({\rm R \mbox{-}Proj})$ is $\aleph_1$-compactly generated, with the category $K^+ ({\rm R \mbox{-}proj})$ of left bounded complexes of finitely generated projective $R$-modules providing an essentially small class of such generators. Another proof of Neeman's theorem is explained, using recent ideas of Christensen...

Topics: Rings and Algebras, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1704.00233

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4.0

Apr 1, 2017
04/17

Apr 1, 2017
by
Mohamed Louzari; L'moufadal Benyakoub

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Let $(\sigma,\delta)$ be a quasi derivation of a ring $R$ and $M_R$ a right $R$-module. In this paper, we introduce the notion of $(\sigma,\delta)$-skew McCoy modules which extends the notion of McCoy modules and $\sigma$-skew McCoy modules. This concept can be regarded also as a generalization of $(\sigma,\delta)$-skew Armendariz modules. Some properties of this concept are established and some connections between $(\sigma,\delta)$-skew McCoyness and $(\sigma,\delta)$-compatible reduced...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1704.00191