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14
Jun 27, 2018
06/18
by
Mohammad Ashraf; Ghulam Mohammad
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Let $R=\mathbb{Z}_4+u\mathbb{Z}_4,$ where $\mathbb{Z}_4$ denotes the ring of integers modulo $4$ and $u^2=0$. In the present paper, we introduce a new Gray map from $R^n$ to $\mathbb{Z}_{4}^{2n}.$ We study $(1+2u)$-constacyclic codes over $R$ of odd lengths with the help of cyclic codes over $R$. It is proved that the Gray image of $(1+2u)$-constacyclic codes of length $n$ over $R$ are cyclic codes of length $2n$ over $\mathbb{Z}_4$. Further, a number of linear codes over $\mathbb{Z}_4$ as the...
Topics: Information Theory, Rings and Algebras, Mathematics, Computing Research Repository
Source: http://arxiv.org/abs/1504.03445
4
4.0
Jun 29, 2018
06/18
by
Ruipu Bai; Yansha Gao; Zhenheng Li
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We study an extension algebra $A$ from two given $3$-Lie algebras $M$ and $H$, and discuss the extensibility of a pair of derivations, one from the derivation algebra of $M$ and the other from that of $H$, to a derivation of $A$. In particular, we give conditions for such an extension to be a $3$-Lie algebra, and provide necessary and sufficient conditions of the pair of derivations to be extendable.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1607.08276
4
4.0
Jun 29, 2018
06/18
by
Toke Meier Carlsen
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We characterise when the Leavitt path algebras over $\mathbb{Z}$ of two arbitrary countable directed graphs are $*$-isomorphic by showing that two Leavitt path algebras over $\mathbb{Z}$ are $*$-isomorphic if and only if the corresponding graph groupoids are isomorphic (if and only if there is a diagonal preserving isomorphism between the corresponding graph $C^*$-algebras). We also prove that any $*$-homomorphism between two Leavitt path algebras over $\mathbb{Z}$ maps the diagonal to the...
Topics: Operator Algebras, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1601.00777
5
5.0
Jun 29, 2018
06/18
by
P. Niroomand; M. Parvizi
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In the present context, we investigate to obtain some more results about $2$-nilpotent multiplier $\mathcal{M}^{(2)}(L)$ of a finite dimensional nilpotent Lie algebra $L$. For instance, we characterize the structure of $\mathcal{M}^{(2)}(H)$ when $H$ is a Heisenberg Lie algebra. Moreover, we give some inequalities on $ \mathrm{dim}~ \mathcal{M}^{(2)}(L)$ to reduce a well known upper bound on $2$-nilpotent multiplier as much as possible. Finally, we show that $H(m)$ is 2-capable if and only if...
Topics: Commutative Algebra, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1610.05581
10
10.0
Jun 30, 2018
06/18
by
Diogo Diniz Pereira da Silva e Silva
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We consider the algebra $E\otimes E$ over an infinite field equipped with a $\mathbb{Z}_2$-grading where the canonical basis is homogeneous and prove that in various cases the graded identites are just the ordinary ones. If the grading is a non-canonical grading obtained as a quotient grading of the natural $\mathbb{Z}_2\times\mathbb{Z}_2$-grading we exhibit a basis for the graded identities.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1407.1305
4
4.0
Jun 29, 2018
06/18
by
Shavkat Ayupov; Karimbergen Kudaybergenov
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We prove that every $2$-local automorphism on a finite-dimensional semi-simple Lie algebra $\mathcal{L}$ over an algebraically closed field of characteristic zero is an automorphism. We also show that each finite-dimensional nilpotent Lie algebra $\mathcal{L}$ with $\dim \mathcal{L}\geq 2$ admits a $2$-local automorphism which is not an automorphism.
Topics: Operator Algebras, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1602.05187
4
4.0
Jun 29, 2018
06/18
by
S. Garibaldi
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The five exceptional simple Lie algebras over the complex number are included one within the other as $G_2 \subset F_4 \subset E_6 \subset E_7 \subset E_8$. The biggest one, $E_8$, is in many ways the most mysterious. This article surveys what is known about it including many recent results, focusing on the point of view of Lie algebras and algebraic groups over fields.
Topics: Group Theory, Representation Theory, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1605.01721
4
4.0
Jun 30, 2018
06/18
by
Alexandr N. Zubkov
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The purpose of this paper is to prove necessary and sufficient criteria for a $GL(m|n)$-supermodule to have a good or Weryl filtration. We also introduce the notion of a Steinberg supermodule analogous to the classical notion of Steinberg module. We prove that the Steinberg supermodule inherits some properties of the Steinberg module. Some new series of finite-dimensional tilting supermodules are found.
Topics: Mathematics, Rings and Algebras, Representation Theory
Source: http://arxiv.org/abs/1406.3757
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11
Jun 30, 2018
06/18
by
Allan Berele
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We generalize the notion of trace identity to $J$-trace. Our main result is that all $J$-traces of $M_{n,n}$ are consequence of those of degree $\frac12n(n + 3)$. This also gives an indirect description of the queer trace identities of $M_n(E)$.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1408.0837
3
3.0
Jun 29, 2018
06/18
by
Nathan Brownlowe; Adam P W Sørensen
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For a commutative ring $R$ with unit we investigate the embedding of tensor product algebras into the Leavitt algebra $L_{2,R}$. We show that the tensor product $L_{2,\mathbb{Z}}\otimes L_{2,\mathbb{Z}}$ does not embed in $L_{2,\mathbb{Z}}$ (as a unital $*$-algebra). We also prove a partial non-embedding result for the more general $L_{2,R} \otimes L_{2,R}$. Our techniques rely on realising Thompson's group $V$ as a subgroup of the unitary group of $L_{2,R}$.
Topics: Operator Algebras, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1603.03618
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15
Jun 27, 2018
06/18
by
Martin Schlichenmaier
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We show how the recently again discussed $N$-point Witt, Virasoro, and affine Lie algebras are genus zero examples of the multi-point versions of Krichever--Novikov type algebras as introduced and studied by Schlichenmaier. Using this more general point of view, useful structural insights and an easier access to calculations can be obtained. The concept of almost-grading will yield information about triangular decompositions which are of importance in the theory of representations. As examples...
Topics: Mathematical Physics, High Energy Physics - Theory, Algebraic Geometry, Rings and Algebras, Quantum...
Source: http://arxiv.org/abs/1505.00736
5
5.0
Jun 29, 2018
06/18
by
Bijan Davvaz; Zahra Nazemian; Ashish K. Srivastava
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This paper studies similarities and differences between the classes of rings over which each simple module is injective and rings over which each simple module is $\Sigma$-injective. The rings in the former class are called $V$-rings and the rings in the latter class are called $\Sigma$-$V$ rings. We have obtained analogues of various well-known results about $V$-rings for $\Sigma$-$V$ rings. Motivated by a conjecture of Kaplansky, Fisher asked if a prime right $V$-ring is right primitive....
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1605.05009
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7.0
Jun 30, 2018
06/18
by
Jan Šaroch
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We prove that the property Add$(M)\subseteq$ Prod$(M)$ characterizes $\Sigma$-algebraically compact modules if $|M|$ is not $\omega$-measurable. Moreover, under a large cardinal assumption, we show that over any ring $R$ where $|R|$ is not $\omega$-measurable, any free module $M$ of $\omega$-measurable rank satisfies Add$(M)\subseteq$ Prod$(M)$, hence the assumption on $|M|$ cannot be dropped in general (e.g. over small non-right perfect rings). In this way, we extend results from a recent...
Topics: Mathematics, Logic, Rings and Algebras
Source: http://arxiv.org/abs/1406.0098
3
3.0
Jun 29, 2018
06/18
by
Yatir Halevi
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We describe the $\infty$-definable subsemigroups of $M_2(\mathbb{C})$ and show directly that they are intersections of definable subsemigroups.
Topics: Logic, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1607.03603
3
3.0
Jun 29, 2018
06/18
by
Hossein Mohades
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The definition of a holomorphic function over a general measurable space $S$ endowed with a Markov process is defined by Zeghib and Barre. In this article we consider holomorphic functions over graphs whose ranges are a given finite field or a cyclic group. Also we consider a relation between $\mathbb{C}$-holomorphic functions over regular trees and the field of $p$-adic numbers.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1612.09036
3
3.0
Jun 30, 2018
06/18
by
Eliyahu Matzri
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Let $A$ be the generic abelian crossed product with respect to $\mathbb{Z}_3\times \mathbb{Z}_3$, in this note we show that $A$ is similar to the tensor product of 4 symbol algebras (3 of degree 9 and one of degree 3) and if $A$ is of exponent $3$ it is similar to the product of 31 symbol algebras of degree $3$. We then use \cite{RS} to prove that if $A$ is any algebra of degree $9$ then $A$ is similar to the product of $35840$ symbol algebras ($8960$ of degree $3$ and $26880$ of degree $9$)...
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1402.0328
10
10.0
Jun 30, 2018
06/18
by
Luís Felipe Gonçalves Fonseca
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Let $F$ be a finite field with characteristic $p > 2$ and let $G$ be the unitary Grassmann algebra generated by an infinite dimensional vector space $V$ over $F$. In this paper, we determine a basis of the $\mathbb{Z}_{2}$-graded polynomial identities for any non-trivial $\mathbb{Z}_{2}$-grading such that a basis of $V$ is homogeneous in this grading.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1403.0888
7
7.0
Jun 29, 2018
06/18
by
Giuseppe Baccella; Leonardo Spinosa
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If $R$ is a regular and semiartinian ring, it is proved that the following conditions are equivalent: (1) $R$ is unit-regular, (2) every factor ring of $R$ is directly finite, (3) the abelian group $K_0(R)$ is free and admits a basis which is in a canonical one to one correspondence with a set of representatives of simple right $R$-modules. For the class of semiartinian and unit-regular rings the canonical partial order of $K_0(R)$ is investigated and the directed abelian groups which are...
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1605.04606
3
3.0
Jun 29, 2018
06/18
by
Armando Reyes; Héctor Suárez
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The aim of this paper is to investigate a general notion of $\sigma$-PBW extensions over Armendariz rings. As an application, the properties of being Baer, quasi-Baer, p.p. and p.q.-Baer are established for these extensions. We generalize several results in the literature for Ore extensions of injective type and skew PBW extensions.
Topics: Operator Algebras, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1611.01562
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10.0
Jun 29, 2018
06/18
by
Indu R. U. Churchill; M. Elhamdadi; M. Green; A. Makhlouf
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The purpose of this paper is to introduce and study the notions of $f$-rack and $f$-quandle which are obtained by twisting the usual equational identities by a map. We provide some key constructions, examples and classification of low order $f$-quandles. Moreover, we define modules over $f$-racks, discuss extensions and define a cohomology complex for $f$-quandles.
Topics: Quantum Algebra, Algebraic Topology, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1606.00353
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22
Jun 28, 2018
06/18
by
Zengqiang Lin
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Let $\mathcal{C}$ be a $k$-linear category with split idempotents, and $\Sigma:\mathcal{C}\rightarrow\mathcal{C}$ an automorphism. We show that there is an $n$-angulated structure on $(\mathcal{C},\Sigma)$ under certain conditions. As an application, we obtain a class of examples of $n$-angulated categories from self-injective algebras.
Topics: Mathematics, Rings and Algebras, Representation Theory
Source: http://arxiv.org/abs/1509.06147
12
12
Jun 27, 2018
06/18
by
Jun Zhao; Liangyun Chen
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In this paper, we define $\omega$-derivations, and study some properties of $\omega$-derivations, with its properties we can structure a new $n$-ary Hom-Nambu algebra from an $n$-ary Hom-Nambu algebra. In addition, we also give derivations and representations of $n$-ary Hom-Nambu algebras.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1505.08168
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8.0
Jun 30, 2018
06/18
by
Adam Chapman
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We study central simple algebras in various ways, focusing on the role of $p$-central subspaces. The first part of my thesis is dedicated to the study of Clifford algebras. The standard Clifford algebra of a given form is the generic associative algebra containing a $p$-central subspace whose exponentiation form is equal to the given form. There is an old question as for whether these algebras have representations of finite rank over the center, and jointly with Daniel Krashen and Max Lieblich...
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1406.0069
5
5.0
Jun 29, 2018
06/18
by
Wolfgang Kimmerle; Leo Margolis
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We consider the question whether a Sylow like theorem is valid in the normalized units of integral group rings of finite groups. After a short survey on the known results we show that this is the case for integral group rings of Frobenius groups. This completes work of M.A. Dokuchaev, S.O. Juriaans and V. Bovdi and M. Hertweck. We analyze projective linear simple groups and show what can be achieved for p-subgroups with known methods.
Topics: Group Theory, Representation Theory, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1605.09599
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7.0
Jun 30, 2018
06/18
by
P. L. Robinson
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Viewing the complex Clifford algebra $C(V)$ of a real inner product space $V$ as a superalgebra, we offer several proofs of the fact that if $W$ is a subspace of the complexification of $V$ then the supercommutant of the Clifford algebra $C(W)$ is precisely the Clifford algebra $C(W^{\perp})$.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1407.1420
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4.0
Jun 30, 2018
06/18
by
P. L. Robinson
texts
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Let $V$ be a real inner product space and $C[V]$ its ${\rm C}^*$ Clifford algebra. We prove that if $Z$ is a subspace of $V$ then $C[Z^{\perp}]$ coincides with the supercommutant of $C[Z]$ in $C[V]$.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1407.3326
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17
Jun 27, 2018
06/18
by
Leon Lampret; Aleš Vavpetič
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We investigate the (co)homological properties of two classes of Lie algebras that are constructed from any finite poset: the solvable class $\frak{gl}^\preceq$ and the nilpotent class $\frak{gl}^\prec$. We confirm the conjecture of Jollenbeck that says: every prime power $p^r\!\leq\!n\!-\!2$ appears as torsion in $H_\ast(\frak{nil}_n;\mathbb{Z})$, and every prime power $p^r\!\leq\!n\!-\!1$ appears as torsion in $H_\ast(\frak{sol}_n;\mathbb{Z})$. If $\preceq$ is a bounded poset, then the...
Topics: Combinatorics, Rings and Algebras, Mathematics, Algebraic Topology
Source: http://arxiv.org/abs/1504.07743
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6.0
Jun 29, 2018
06/18
by
Mahouton Norbert Hounkonnou; Gbêvèwou Damien Houndedji
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The (co)associative, partially (co)associative and totally (co)associative $3$-ary (co) algebras and infinitesimal bialgebras are constructed and discussed. Their trimodules and matched pairs are defined and completely characterized. The main structural properties and relations are also deduced and analyzed.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1608.07964
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6.0
Jun 30, 2018
06/18
by
Tristan Bice
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We generalize some basic C*-algebra and von Neumann algebra theory on hereditary C*-subalgebras and projections. In particular, we extend Murray-von Neumann equivalence from projections to *-annihilators and show that several of its important properties also extend from von Neumann algebras to proper *-semigroups. Furthermore, we show how to obtain *-annihilator decompositions of a proper *-semigroup that correspond to classical von Neumann algebra type decompositions.
Topics: Mathematics, Rings and Algebras, Operator Algebras
Source: http://arxiv.org/abs/1404.1589
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5.0
Jun 30, 2018
06/18
by
Yuefeng Gao; Jianlong Chen; Yuanyuan Ke
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In this paper, we investigate *-DMP elements in $*$-semigroups and $*$-rings. The notion of *-DMP element was introduced by Patr\'{i}cio in 2004. An element $a$ is *-DMP if there exists a positive integer $m$ such that $a^{m}$ is EP. We first characterize *-DMP elements in terms of the \{1,3\}-inverse, Drazin inverse and pseudo core inverse, respectively. Then, we give the pseudo core decomposition utilizing the pseudo core inverse, which extends the core-EP decomposition introduced by Wang for...
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1701.00621
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5.0
Jun 29, 2018
06/18
by
Tristan Bice
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We examine a number of *-ring orderings, generalizing classical properties of *-positive elements to *-accretives. We also examine *-rings satisfying versions of Blackadar's property (SP), generalizing some basic properties of Rickart *-rings to Blackadar *-rings.
Topics: Operator Algebras, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1601.02270
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17
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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11
Jun 27, 2018
06/18
by
Hojjat Mostafanasab
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In this paper, we give some characterizations of the ring $R[x,y,\rho,\theta]$ where R is a commutative ring. We investigate 2-D skew $(\lambda_1,\lambda_2)$-constacyclic codes.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1505.02238
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5.0
Jun 30, 2018
06/18
by
Tiffany Burch; Meredith Harris; Allison McAlister; Elyse Rogers; Ernie Stitzinger; S. McKay Sullivan
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We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and super solvable. These results hold in Lie algebras and in general for groups.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1407.8227
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4.0
Jun 29, 2018
06/18
by
Daniel Chan
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Tilting bundles $\mathcal{T}$ on a weighted projective line $\mathbb{X}$ have been intensively studied by representation theorists since they give rise to a derived equivalence between $\mathbb{X}$ and the finite dimensional algebra End $\mathcal{T}$. A classical result states that if End $\mathcal{T}$ is hereditary, then $\mathbb{X}$ is Fano and conversely, for every Fano weighted projective line, there exists a tilting bundle $\mathcal{T}$ with End $\mathcal{T}$ hereditary. In this paper, we...
Topics: Representation Theory, Algebraic Geometry, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1604.06141
3
3.0
Jun 30, 2018
06/18
by
Askar Dzhumadil'daev
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We show that a space of one variable differential operators of order $p$ admits non-trivial $2p$-commutator and the number $2p$ here can not be improved.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1401.1730
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7.0
Jun 29, 2018
06/18
by
A. Rezaei-Aghdam; L. Sedghi-Ghadim
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In this paper by use of cohomology complex of $3$-Leibniz algebras, the definitions of Leibniz bialgebras (and Lie bialgebras) are extended for the case of $3$-Leibniz algebras. Many theorems about Leibniz bialgebras are extended and proved for the case of $3$-Leibniz bialgebras ($3$-Lie bialgebras). Moreover a new theorem on the correspondence between $3$-Leibniz bialgebra and its associated Leibniz bialgebra is proved. $3$-Lie bialgebra as particular case of the $3$-Leibniz bialgebra is...
Topics: Mathematical Physics, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1604.04475
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3.0
Jun 30, 2018
06/18
by
Shohei Izawa
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We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove that for a finite algebra, it has an irredundant non-refinable cover consists of primal algebras if and only if it is the both congruence primal and arithmetical. Finally, we obtain combinatorial description of congruence primal arithmetical algebras.
Topics: Mathematics, Category Theory, Logic, Rings and Algebras
Source: http://arxiv.org/abs/1406.6546
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11
Jun 29, 2018
06/18
by
Nik Weaver
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Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under the formation of Hermitian adjoints. We prove that if n is sufficiently large then there exists a rank k orthogonal projection P such that dim(PVP) = 1 or k^2.
Topics: Functional Analysis, Quantum Physics, Rings and Algebras, Mathematics, Combinatorics, Operator...
Source: http://arxiv.org/abs/1601.01259
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4.0
Jun 28, 2018
06/18
by
Alfredo Nájera Chávez
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We construct a 2-Calbi-Yau realization of various finite-type cluster algebras with coefficients using completed orbit categories associated to Frobenius categories. Namely, the Frobenius categories we consider are the categories of representable functors over (a quotient of) the Nakajima category associated to a Dynkin diagram. In particular, we are able to categorify all finite-type skew-symmetric cluster algebras with universal coefficients. Along the way, we classify the standard Frobenius...
Topics: Commutative Algebra, Category Theory, Rings and Algebras, Representation Theory, Mathematics
Source: http://arxiv.org/abs/1512.07939
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4.0
Jun 30, 2018
06/18
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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Jun 29, 2018
06/18
by
Apoorva Khare; Akaki Tikaradze
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We compute the $k$th power-sum polynomials (for $k \geqslant 0$) over an arbitrary finite ring $R$, obtained by summing the $k$th powers of $(T+r)$ for $r \in R$. For $R$ non-commutative, this extends the work of Brawley--Carlitz--Levine [Duke Math. J. 41], and resolves a conjecture by Fortuny, Grau, Oller-Marcen, and Rua (2015). For $R$ commutative, our results bring together two classical programs in the literature: von Staudt--Clausen type results on computing zeta values in finite rings [J....
Topics: Number Theory, Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1606.05271
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10.0
Jun 27, 2018
06/18
by
Ali Assem
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In 2009, J. Wood [15] proved that Frobenius bimodules have the extension property for symmetrized weight compositions. Later, in [9], it was proved that having a cyclic socle is sufficient for satisfying the property, while the necessity remained an open question. Here, landing in Midway, the necessity is proved, a module alphabet RA has the extension property for symmetrized weight compositions built on AutR(A) is necessarily having a cyclic socle.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1505.00466
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49
Jun 30, 2018
06/18
by
Neville Fogarty; Heide Gluesing-Luerssen
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We introduce circulant matrices that capture the structure of a skew-polynomial ring F[x;\theta] modulo the left ideal generated by a polynomial of the type x^n-a. This allows us to develop an approach to skew-constacyclic codes based on such circulants. Properties of these circulants are derived, and in particular it is shown that the transpose of a certain circulant is a circulant again. This recovers the well-known result that the dual of a skew-constacyclic code is a constacyclic code...
Topics: Mathematics, Rings and Algebras, Computing Research Repository, Information Theory
Source: http://arxiv.org/abs/1408.5445
3
3.0
Jun 29, 2018
06/18
by
Timothy Kohl
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For $p$ a prime and $a\in\mathbb{Q}$, where $a$ is not a $p^n$-th power of any rational number, the extension $\mathbb{Q}(w_n)/\mathbb{Q}$ where $w_n=\root p^n \of a$ is separable but non-normal. The Hopf-Galois theory for separable extensions was determined by Greither and Pareigis, and the specific classification for radical extensions such as these by the author. In this work we extend this theory to a certain class of profinite extensions, namely those formed from the union of these...
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1610.04630
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5.0
Jun 30, 2018
06/18
by
Cristina Flaut
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In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.
Topics: Mathematics, Rings and Algebras
Source: http://arxiv.org/abs/1404.1513
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4.0
Jun 30, 2018
06/18
by
Kyungyong Lee; Li Li; Matthew R. Mills
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We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra.
Topics: Mathematics, Rings and Algebras, Combinatorics
Source: http://arxiv.org/abs/1409.8177
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Jun 26, 2018
06/18
by
Koenraad M. R. Audenaert
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We prove that for positive semidefinite matrices $A$ and $B$ the following determinantal inequality holds: \[ \det(I+A\#B)\le \det(I+A^{1/2}B^{1/2}), \] where $A\#B$ is the geometric mean of $A$ and $B$. We apply this inequality to the study of interpolation methods in diffusion tensor imaging.
Topics: Mathematics, Statistics Theory, Statistics, Rings and Algebras
Source: http://arxiv.org/abs/1502.06902
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3.0
Jun 29, 2018
06/18
by
Ashish Gupta; Arnab Dey Sarkar
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The Gelfand--Kirillov dimension has gained importance since its introduction as an tool in the study of non-commutative infinite dimensional algebras and their modules. In this paper we show a dichotomy for the Gelfand--Kirillov dimension of simple modules over certain simple rings of differential operators.
Topics: Rings and Algebras, Mathematics
Source: http://arxiv.org/abs/1612.05303
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4.0
Jun 29, 2018
06/18
by
Jonathan S Brown
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We define the Drinfeld generators for $Y_3^+$, the twisted Yangian associated to the Lie algebra $\mathfrak{so}_3(\mathbb{C})$. This allows us to define shifted twisted Yangians, which are certain subalgebras of $Y_3^+$. We show that there are families of homomorphisms from the shifted twisted Yangians in $Y_3^+$ to the universal enveloping algebras of various orthogonal and symplectic Lie algebras, and we conjecture that the images of these homomorphisms are isomorphic to various finite...
Topics: Rings and Algebras, Representation Theory, Quantum Algebra, Mathematics
Source: http://arxiv.org/abs/1601.05701
