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3.0

Jun 30, 2018
06/18

by
Judith J. McDonald; Pietro Paparella

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Arising from the classification of the matrix-roots of a nonnegative imprimitive irreducible matrix, we present results concerning the Jordan chains of an $h$-cyclic matrix. We also present ancillary results applicable to nonnegative imprimitive irreducible matrices and demonstrate these results via examples.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1407.4486

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5.0

Jun 30, 2018
06/18

by
Jia Zhou; Liangyun Chen; Yao Ma

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In this paper, we give some basic properties of the generalized derivation algebra ${\rm GDer}(L)$ of a Hom-Lie superalgebra $L$. In particular, we prove that ${\rm GDer}(L) = {\rm QDer}(L) + {\rm QC}(L)$, the sum of the quasiderivation algebra and the quasicentroid. We also prove that ${\rm QDer}(L)$ can be embedded as derivations in a larger Hom-Lie superalgebra.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1406.1578

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4.0

Jun 30, 2018
06/18

by
Rod Gow

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Let q be a power of a prime and let V be a vector space of finite dimension n over the field of order q. Let Bil(V) denote the set of all bilinear forms defined on V x V, let Symm(V) denote the subspace of Bil(V) consisting of symmetric bilinear forms, and Alt(V) denote the subspace of alternating bilinear forms. Let M denote a subspace of any of the spaces Bil(V), Symm(V), or Alt(V). In this paper we investigate hypotheses on the rank of the non-zero elements of M which lead to reasonable...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1703.07266

2
2.0

Jun 29, 2018
06/18

by
Jean-Luc Marichal; Bruno Teheux

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The so-called generalized associativity functional equation G(J(x,y),z) = H(x,K(y,z)) has been investigated under various assumptions, for instance when the unknown functions G, H, J, and K are real, continuous, and strictly monotonic in each variable. In this note we investigate the following related problem: given the functions J and K, find every function F that can be written in the form F(x,y,z) = G(J(x,y),z) = H(x,K(y,z)) for some functions G and H. We show how this problem can be solved...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1607.08435

2
2.0

Jun 29, 2018
06/18

by
Lina Song; Rong Tang

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In this paper, we introduce the notion of a derivation of a Hom-Lie algebra and construct the corresponding strict Hom-Lie 2-algebra, which is called the derivation Hom-Lie 2-algebra. As applications, we study non-abelian extensions of Hom-Lie algebras. We show that iso- morphism classes of diagonal non-abelian extensions of a Hom-Lie algebra g by a Hom-Lie algebra h are in one-to-one correspondence with homotopy classes of morphisms from g to the derivation Hom-Lie 2-algebra DER(h).

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1611.01340

4
4.0

Jun 30, 2018
06/18

by
Judith J. McDonald; Pietro Paparella

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Using matrix function theory, Perron-Frobenius theory, combinatorial matrix theory, and elementary number theory, we characterize, classify, and describe in terms of the Jordan canonical form the matrix pth-roots of imprimitive irreducible nonnegative matrices. Preliminary results concerning the matrix roots of reducible matrices are provided as well.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1407.4487

2
2.0

Jun 30, 2018
06/18

by
Shervin Sahebi; Venus Rahmani

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Let R be a 2 torsion free semiprime ring and d a nonzero derivation. Further let A = O(R) be the orthogonal completion of R and B = B(C) the Boolean ring of C where C be the extended centroid of R. We show that if a[[d(x),x]^n- [y, d(y)]^m]^t = 0 such that a in R for all x, y in R, where m, n, t > 0 are fixed integers, then there exists an idempotent e in B such that eA is a commutative ring and d induce a zero derivation on (1-e)A.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1409.5951

2
2.0

Jun 30, 2018
06/18

by
Viktor Abramov

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We propose a notion of a super n-Lie algebra and construct a super n-Lie algebra with the help of a given binary super Lie algebra which is equipped with an analog of a supertrace. We apply this approach to the super Lie algebra of a Clifford algebra with even number of generators and making use of a matrix representation of this super Lie algebra given by a supermodule of spinors we construct a series of super 3-Lie algebras labeled by positive even integers.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1410.5923

2
2.0

Jun 30, 2018
06/18

by
Emira Akkurt; Mustafa Akkurt

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Automorphisms of structural matrix algebras in block upper triangular form has been studied recently in \cite{Akkurt E-M Barker 2}, and this work is a follow-up paper of that study. The aim of this paper is to explain the topic in a much clearer and more comprehensible way by presenting some examples.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1411.0438

2
2.0

Jun 30, 2018
06/18

by
Clas Löfwall

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In [7, Papadima and Suciu, When does the associated graded Lie algebra of an arrangement group decompose? Comment. Math. Helv. {\bf 81:4} (2006), 859--875] it is proved that the holonomy Lie algebra of an arrangement of hyperplanes through origo decomposes as a direct product of Lie algebras in degree at least two if and only if a certain (computable) condition is fulfilled. We prove similar results for a class of Lie algebras which is a generalization of the holonomy Lie algebras. The proof...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1412.3068

4
4.0

Jun 29, 2018
06/18

by
Uriya A. First; Zinovy Reichstein

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A classical theorem of Forster asserts that a finite module $M$ of rank $\leq n$ over a Noetherian ring of Krull dimension $d$ can be generated by $n + d$ elements. We prove a generalization of this result, with "module" replaced by "algebra". Here we allow arbitrary finite algebras, not necessarily unital, commutative or associative. Forster's theorem can be recovered as a special case by viewing a module as an algebra where the product of any two elements is $0$.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1610.08156

2
2.0

Jun 30, 2018
06/18

by
Daowei Lu; Shuanhong Wang

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Let $(H,\alpha)$ be a monoidal Hom-Hopf algebra, and $(A,\beta)$ a Hom-algebra. In this paper the crossed product $(A\#_{\sigma}H,\beta\otimes\alpha)$ is constructed, which is a Hom-algebra. Then we will introduce the notion of cleft extensions and Galois extensions, and prove that a crossed product is equivalent to a cleft extension and both are Galois extensions with normal basis property.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1405.7528

2
2.0

Jun 30, 2018
06/18

by
Lindsey Bosko-Dunbar; Matthew Burke; Jonathan Dunbar; J. T. Hird; Kristen Stagg Rovira

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A classification exists for Lie algebras whose nilradical is the triangular Lie algebra $T(n)$. We extend this result to a classification of all solvable Leibniz algebras with nilradical $T(n)$. As an example we show the complete classification of all Leibniz algebras whose nilradical is $T(4)$.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1407.7455

2
2.0

Jun 29, 2018
06/18

by
Paul Gilmartin

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Let $k$ be a field and let $H$ denote a pointed Hopf $k$-algebra with antipode $S$. We are interested in determining the order of $S$. Building on the work done by Taft and Wilson $[7]$, we define an invariant for $H$, denoted $m_{H}$, and prove that the value of this invariant is connected to the order of $S$. In the case where $\operatorname{char}k=0$, it is shown that if $S$ has finite order then it is either the identity or has order $2m_{H}$. If in addition $H$ is assumed to be coradically...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1611.03480

2
2.0

Jun 30, 2018
06/18

by
Gen Li; Yuantao Gu

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For a matrix ${\bf A}$ with linearly independent columns, this work studies to use its normalization $\bar{\bf A}$ and ${\bf A}$ itself to approximate its orthonormalization $\bf V$. We theoretically analyze the order of the approximation errors as $\bf A$ and $\bar{\bf A}$ approach ${\bf V}$, respectively. Our conclusion is able to explain the fact that a high dimensional Gaussian matrix can well approximate the corresponding truncated Haar matrix. For applications, this work can serve as a...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1701.00711

2
2.0

Jun 30, 2018
06/18

by
Pedro A. Guil Asensio; Berke Kalebogaz; Ashish K. Srivastava

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In this paper we study the Schr\"{o}der-Bernstein problem for modules. We obtain a positive solution for the Schr\"{o}der-Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes. In the particular cases of injective envelopes and pure-injective envelopes, we are able to extend it further and we show that the...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1703.04787

2
2.0

Jun 30, 2018
06/18

by
G. -S. Zhou; D. -M. Lu

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We show certain invariants of graded algebras of which all obstructions are Lyndon words and provide some methods to construct Artin-Schelter regular algebras from a closed set of Lyndon words.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1403.0385

2
2.0

Jun 30, 2018
06/18

by
Mohammad Vahdani Mehrabadi; Shervin Sahebi; Hamid H. S. Javadi

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We introduce Central McCoy rings, which are a generalization of McCoy rings and investigate their properties. For a ring R, we prove that R is right Central McCoy if and only if the polynomial ring R[x] is right Central McCoy. Also, we give some examples to show that if R is right Central McCoy, then Mn(R) and Tn(R) are not necessary right Central McCoy, but Dn(R) and Vn(R) are right Central McCoy, where Dn(R) and Vn(R) are the subrings of the triangular matrices with constant main diagonal and...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1410.3243

2
2.0

Jun 29, 2018
06/18

by
Dušan Repovš; Mikhail Zaicev

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We study polynomial identities of algebras with adjoined external unit. For a wide class of algebras we prove that adjoining external unit element leads to increasing of PI-exponent precisely to 1. We also show that any real number from the interval [2,3] can be realized as PI-exponent of some unital algebra.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1602.02942

3
3.0

Jun 30, 2018
06/18

by
Shuang-jian Guo; Xiu-li Chen

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In this paper, we prove a Maschke type theorem for the category of relative Hom-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the $(H, \a)$-coaction to be separable. This leads to a generalized notion of integrals.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1411.7204

3
3.0

Jun 30, 2018
06/18

by
Yan Cao; Liangyun Chen

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We study the structures of arbitrary split Leibniz triple systems. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of $T$ being of maximal length, the simplicity of the Leibniz triple systems is characterized.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1411.7026

2
2.0

Jun 29, 2018
06/18

by
Lisa Orloff Clark; Yosafat E. P. Pangalela

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In this article, we introduce Cohn path algebras of higher-rank graphs. We prove that for a higher-rank graph $\Lambda $, there exists a higher-rank graph $T\Lambda $ such that the Cohn path algebra of $\Lambda $ is isomorphic to the Kumjian-Pask algebra of $T\Lambda $. We then use this isomorphism and properties of Kumjian-Pask algebras to study Cohn path algebras. This includes proving a uniqueness theorem for Cohn path algebras.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1604.00072

2
2.0

Jun 29, 2018
06/18

by
Mai Hoang Bien; Johan Öinert

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In this article we give a characterization of left (right) quasi-duo differential polynomial rings. In particular, we show that a differential polynomial ring is left quasi-duo if and only if it is right quasi-duo. This yields a partial answer to a question posed by Lam and Dugas in 2005. We provide non-trivial examples of such rings and give a complete description of the maximal ideals of an arbitrary quasi-duo differential polynomial ring. Moreover, we show that there is no left (right)...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1607.03178

2
2.0

Jun 28, 2018
06/18

by
Péter E. Frenkel

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We determine minimal Cayley--Hamilton and Capelli identities for matrices over a Grassmann algebra of finite rank. For minimal standard identities, we give lower and upper bounds on the degree. These results improve on upper bounds given by L.\ M\'arki, J.\ Meyer, J.\ Szigeti, and L.\ van Wyk in a recent paper.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1511.05540

2
2.0

Jun 30, 2018
06/18

by
Vladimir Gorbatsevich

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The Lie algebras over the algebra of dual numbers are introduced and investigated.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1701.04310

2
2.0

Jun 30, 2018
06/18

by
Jiafeng Lü; Sei-Qwon Oh; Xingting Wang; Xiaolan Yu

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It is proved that the Poisson enveloping algebra of a double Poisson-Ore extension is an iterated double Ore extension. As an application, properties that are preserved under iterated double Ore extensions are invariants of the Poisson enveloping algebra of a double Poisson-Ore extension.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1702.00647

2
2.0

Jun 30, 2018
06/18

by
Jan A. Bergstra; Alban Ponse

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Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with "a" that propagates through all operations of the meadow signature (this additional value can be interpreted as an error element). We provide a basis theorem for so-called common cancellation meadows of characteristic zero, that is, common meadows of characteristic zero that admit a certain cancellation law.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1406.6878

2
2.0

Jun 30, 2018
06/18

by
Shuangjian Guo; Shengxiang Wang

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Let A#_{\alpha, \omega}H be a partial crossed product. In this paper, we first generalize the theorem about the existence of an enveloping action to twisted partial actions. Second, we construct a Morita context between the partial crossed product and the crossed product related to the enveloping action. Furthermore, we discuss equivalences of partial crossed products Finally, we investigate when A\subset A#_{\alpha, \omega}H becomes a separable extension.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1412.4552

2
2.0

Jun 30, 2018
06/18

by
Dennis Presotto; Louis de Thanhoffer de Völcsey

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In this note we consider a notion of relative Frobenius pairs of commutative rings $S/R$. To such a pair, we associate an $\mathbb{N}$-graded $R$-algebra $\Pi_R(S)$ which has a simple description and coincides with the preprojective algebra of a quiver with a single central node and several outgoing edges in the split case. If the rank of $S$ over $R$ is 4 and $R$ is noetherian, we prove that $\Pi_R(S)$ is itself noetherian and finite over its center and that each $\Pi_R(S)_d$ is finitely...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1412.6899

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2.0

Jun 28, 2018
06/18

by
Demba Barry

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We study possible decompositions of totally decomposable algebras with involution, that is, tensor products of quaternion algebras with involution. In particular, we are interested in decompositions in which one or several factors are the split quaternion algebra $M_2(F)$, endowed with an orthogonal involution. Using the theory of gauges, developed by Tignol-Wadsworth, we construct examples of algebras isomorphic to a tensor product of quaternion algebras with $k$ split factors, endowed with an...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1512.01083

3
3.0

Jun 29, 2018
06/18

by
Jaime Castro Pérez; Mauricio Medina Bárcenas; José Ríos Montes; Angel Zaldívar

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In this article we study the behavior of left QI-rings under perfect localizations. We show that a perfect localization of a left QI-ring is a left QI-ring. We prove that Boyle's conjecture is true for left QI-rings with finite Gabriel dimension such that the hereditary torsion theory generated by semisimple modules is perfect. As corollary we get that Boyle's conjecture is true for left QI-rings which satisfy the restricted left socle condition, this result was proved first by C. Faith in...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1611.04672

3
3.0

Jun 30, 2018
06/18

by
Shuanhong Wang

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In this paper we study twisted algebras of multiplier Hopf ($^*$-)algebras which generalize all kinds of smash products such as generalized smash products, twisted smash products, diagonal crossed products, L-R-smash products, two-sided crossed products and two-sided smash products for the ordinary Hopf algebras appeared in [P-O].

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1701.05309

3
3.0

Jun 30, 2018
06/18

by
Michal Hrbek; Pavel Růžička

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A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contain a weak basis. In the paper we study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, (2) regularly weakly based modules over Dedekind domains.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1701.06936

4
4.0

Jun 29, 2018
06/18

by
Artem N. Shevlyakov

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We discuss new problems in universal algebraic geometry and explain them by boolean equations.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1611.00152

2
2.0

Jun 30, 2018
06/18

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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7.0

Jun 29, 2018
06/18

by
Donald W. Barnes

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The Ado-Iwasawa Theorem asserts that a finite-dimensional Lie algebra $L$ over a field $F$ has a finite-dimensional faithful module $V$. There are several extensions asserting the existence of such a module with various additional properties. In particular, Jacobson has proved that if the field has characteristic $p>0$, then there exists a completely reducible such module $V$. I strengthen Jacobson's Theorem, proving that if $L$ has dimension $n$ over the field $F$ of characteristic...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1603.01894

2
2.0

Jun 30, 2018
06/18

by
I. A. Karimjanov; A. Kh. Khudoyberdiyev; B. A. Omirov

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In this paper the description of solvable Lie algebras with triangular nilradicals is extended to Leibniz algebras. It is proven that the matrices of the left and right operators on elements of Leibniz algebra have upper triangular forms. We establish that solvable Leibniz algebra of a maximal possible dimension with a given triangular nilradical is a Lie algebra. Furthermore, solvable Leibniz algebras with triangular nilradicals of low dimensions are classified.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1407.7956

2
2.0

Jun 30, 2018
06/18

by
Huanyin Chen

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A ring is SSP if the sum of two direct summands is a direct summand. A ring has internal cancellation if every its (von Neumann) regular elements are unit-regular. We show that in an SSP ring having internal cancellation, any regular element is special clean. Our main results also imply that for any SSP ring internal cancellation and idempotent stable range $1$ coincide with each other. Internal cancellation over SSP was then characterized by special clean elements.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1408.0781

2
2.0

Jun 30, 2018
06/18

by
Salvatore Siciliano; Hamid Usefi

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Let $L$ be a restricted Lie algebra over a field of characteristic $p>2$ and denote by $u(L)$ its restricted enveloping algebra. We establish when the symmetric or skew elements of $u(L)$ under the principal involution are Lie metabelian.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1411.3713

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4.0

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

4
4.0

Jun 30, 2018
06/18

by
Will Murray

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We show that the Nakayama automorphism of a Frobenius algebra $R$ over a field $k$ is independent of the field (Theorem 4). Consequently, the $k$-dual functor on left $R$-modules and the bimodule isomorphism type of the $k$-dual of $R$, and hence the question of whether $R$ is a symmetric $k$-algebra, are independent of $k$. We give a purely ring-theoretic condition that is necessary and sufficient for a finite-dimensional algebra over an infinite field to be a symmetric algebra (Theorem 7)....

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1402.4559

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3.0

Jun 30, 2018
06/18

by
David E. Radford

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We revisit a class of examples described in the original paper on biproducts, expand the class, and provide a detailed analysis of the coalgebra and algebra structures of many of these examples. Connections with the semisimple Hopf algebras of dimension a power of two determined by Kashina are examined. The finite-dimensional non-trivial semisimple cosemisimple Hopf algebras we construct are shown to be lower cosolvable. Some of these have one proper normal Hopf subalgebra and are not lower...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1402.4714

2
2.0

Jun 30, 2018
06/18

by
Secil Ceken; John Palmieri; Yanhua Wang; James Zhang

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We use the discriminant to determine the automorphism groups of some noncommutative algebras, and we prove that a family of noncommutative algebras has tractable automorphism groups.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1401.0793

2
2.0

Jun 28, 2018
06/18

by
Ioannis Tsartsaflis

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An $n$-dimensional Lie algebra $\mathfrak{g}$ over a field $\mathbb{F}$ of characteristic two is said to be of Vergne type if there is a basis $e_1,\dots,e_n$ such that $[e_1,e_i]=e_{i+1}$ for all $2\leq i \leq n-1$ and $[e_i,e_j] = c_{i,j}e_{i+j}$ for some $c_{i,j} \in \mathbb{F}$ for all $i,j \ge 2$ with $i+j \le n$. We define the algebra $\mathfrak{m}_0$ by its nontrivial bracket relations: $[e_1,e_i]=e_{i+1}, 2\leq i \leq n-1$, and the algebra $\mathfrak{m}_2$: $[e_1, e_i ]=e_{i+1}, 2 \le i...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1511.03132

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5.0

Jun 28, 2018
06/18

by
Ryan Golden; Ilwoo Cho

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In this paper, we study structure theorems of algebras of symmetric functions. Based on a certain relation on elementary symmetric polynomials generating such algebras, we consider perturbation in the algebras. In particular, we understand generators of the algebras as perturbations. From such perturbations, define injective maps on generators, which induce algebra-monomorphisms (or embeddings) on the algebras. They provide inductive structure theorems on algebras of symmetric polynomials. As...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1511.08870

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2.0

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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2.0

Jun 30, 2018
06/18

by
Jiafeng Lü; Xingting Wang; Guangbin Zhuang

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For a Poisson algebra $A$, by exploring its relation with Lie-Rinehart algebras, we prove a Poincar\'e-Birkoff-Witt theorem for its universal enveloping algebra $A^e$. Some general properties of the universal enveloping algebras of Poisson Hopf algebras are studied. Given a Poisson Hopf algebra $B$, we give the necessary and sufficient conditions for a Poisson polynomial algebra $B[x; \alpha, \delta]_p$ to be a Poisson Hopf algebra. We also prove a structure theorem for $B^e$ when $B$ is a...

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1402.2007

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3.0

Jun 30, 2018
06/18

by
Tao Zhang

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The cohomology theory of Lie triple systems in the sense of Yamaguti is studied by means of cohomology of Leibniz algebras in the sense of Loday. The notion of Nijenhuis operators for Lie triple system is introduced to describe trivial deformations. We also study the abelian extensions of Lie triple systems in details.

Topics: Mathematics, Rings and Algebras

Source: http://arxiv.org/abs/1401.7725

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2.0

Jun 29, 2018
06/18

by
Yun Fan; Hualu Liu

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Double circulant matrices are introduced and studied. A formula to compute the rank r of a double circulant matrix is exhibited; and it is shown that any consecutive r rows of the double circulant matrix are linearly independent. As a generalization, multiple circulant matrices are also introduced. Two questions on square double circulant matrices are suggested.

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1601.06872

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4.0

Jun 29, 2018
06/18

by
Lidia Angeleri Hügel; Jan Šaroch; Jan Trlifaj

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A classic result by Bass says that the class of all projective modules is covering, if and only if it is closed under direct limits. Enochs extended the if-part by showing that every class of modules $\mathcal C$, which is precovering and closed under direct limits, is covering, and asked whether the converse is true. We employ the tools developed in [18] and give a positive answer when $\mathcal C = \mathcal A$, or $\mathcal C$ is the class of all locally $\mathcal A ^{\leq \omega}$-free...

Topics: Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1612.01140