arXiv math/04080612004-08-04math.RAmath.QA

Quasi-hom-Lie Algebras, Central Extensions and 2-cocycle-like Identities

Daniel Larsson, Sergei Silvestrov

备注：: 40 pages

英文摘要：

This paper begins by introducing the concept of a quasi-hom-Lie algebra which is a natural generalization of hom-Lie algebras introduced in a previous paper by the authors. Quasi-hom-Lie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by homomorphisms, twisting the Jacobi identity and skew-symmetry. The natural realm for these quasi-hom-Lie algebras is as a generalization-deformation of the Witt algebra $\Witt$ of derivations on the Laurent polynomials $\C[t,t^{-1}]$. We also develop a theory of central extensions for qhl-algebras which can be used to deform and generalize the Virasoro algebra by centrally extending the deformed Witt type algebras constructed here. In addition, we give a number of other interesting examples of quasi-hom-Lie algebras, among them a deformation of the loop algebra.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Polynomial identities and noncommutative versal torsors

To any cleft Hopf Galois object, i.e., any algebra H[t] obtained from a Hopf algebra H by twisting its multiplication with a two-cocycle t, we attach two "universal algebras" A(H,t) and U(H,t). The algebra A(H,t) is obtained by twisting the multiplication of H with the most general two-cocycle u formally cohomologous to t. The cocycle u takes values in the field of rational functions on H. By construction, A(H,t) is a cleft H-Galois extension of a "big" commutative algebra B(H,t). Any "form" of H[t] can be obtained from A(H,t) by a specialization of B(H,t) and vice versa. If the algebra H[t] i…

2007-08-30math.QAmath.RA

Crossed product Hom-Hopf algebras and lazy 2-cocycle

Let $(H,\a)$ be a Hom-Hopf algebra and $(A,\b)$ be a Hom-algebra. In this paper we will construct the Hom-crossed product $(A\#_σH,\bø\a)$, and prove that the extension $A\subseteq A\#_σH$ is actually a Hom-type cleft extension and vice versa. Then we will give the necessary and sufficient conditions to make $(A\#_σH,\bø\a)$ a Hom-Hopf algebra. Finally we will study the lazy 2-cocycle on $(H,\a)$.

2020-04-07math.RA

Normal Hopf subalgebras in cocycle deformations of finite groups

Let $G$ be a finite group and let $π: G \to G'$ be a surjective group homomorphism. Consider the cocycle deformation $L = H^σ$ of the Hopf algebra $H = k^G$ of $k$-valued linear functions on $G$, with respect to some convolution invertible 2-cocycle $σ$. The (normal) Hopf subalgebra $k^{G'} \subseteq k^G$ corresponds to a Hopf subalgebra $L' \subseteq L$. Our main result is an explicit necessary and sufficient condition for the normality of $L'$ in $L$.

2007-11-21math.QAmath.RA

The cocycle condition for multi-pullbacks of algebras

Take finitely many topological spaces and for each pair of these spaces choose a pair of corresponding closed subspaces that are identified by a homeomorpism. We note that this gluing procedure does not guarantee that the building pieces, or the gluings of some pieces, are embedded in the space obtained by putting together all given ingredients. Dually, we show that a certain sufficient condition, called the cocycle condition, is also necessary to guarantee sheaf-like properties of surjective multi-pullbacks of algebras with distributive lattices of ideals.

2012-06-30math.QAmath.RA

具有非退化双线性型的Hom-Poisson超代数与相容的Hom-anti-pre-Poisson超代数

Hom-Poisson superalgebras with nondegenerate bilinear forms and compatible Hom-anti-pre-Poisson superalgebras

University of Sfax（萨法大学）；Faculty of Sciences of Sfax（萨法理学院）；University of Gafsa（加夫萨大学）；Faculty of Sciences Gafsa（加夫萨理学院）

本文引入Hom-anti-Zinbiel超代数等概念，通过非退化超交换上循环建立Hom-Poisson超代数与相容Hom-anti-pre-Poisson超代数的联系，为两类超代数提供统一研究框架。

2026-08-05math.RA

带表示的 Hom-Lie-Yamaguti 代数上由 (2,3)-上循环扭变的 $\mathcal{O}$-算子

Twisting $\mathcal{O}$-operators by $(2,3)$-Cocycle of Hom-Lie-Yamaguti Algebras with Representations

本文在 Hom-Lie-Yamaguti 代数上引入扭变 $\mathcal{O}$-算子，证明其诱导 Hom-Lie-Yamaguti 结构，定义其上同调，并研究其底层 Hom-NS-Lie-Yamaguti 代数及由 Hom-Lie 代数诱导的情形。

2025-02-26math-phmath.MPmath.QA

更多相关论文收起更多论文

Skew Calabi-Yau Algebras and Homological Identities

A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities we prove show (i) how the Nakayama automorphism of a smash product algebra A # H is related to the Nakayama automorphisms of a graded skew Calabi-Yau algebra A and a finite-dimensional Hopf algebra H that acts on it; (ii) how the Nakayama automorphism of a graded twist of A is related to the Nakayama automorphism of A; and (iii) that Nakayama automorphism of…

2013-02-16math.QAmath.RA

On identities in Hom-Malcev algebras

In a Hom-Malcev algebra an identity, equivalent to the Hom-Malcev identity, is found.

2010-11-29math.RA

分次可除代数上的齐合对合及其多项式恒等式

Homogeneous involution on graded division algebras and their polynomial identities

本文研究代数闭域上有限维分次可除代数的齐合对合，计算其带对合的分次多项式恒等式，指出齐合对合在分次多项式恒等式与相容对合研究中自然出现。

2022-07-27math.RA

Cocycle twists of 4-dimensional Sklyanin algebras

We study cocycle twists of a 4-dimensional Sklyanin algebra $A$ and a factor ring $B$ which is a twisted homogeneous coordinate ring. Twisting such algebras by the Klein four-group $G$, we show that the twists $A^{G,μ}$ and $B^{G,μ}$ have very different geometric properties to their untwisted counterparts. For example, $A^{G,μ}$ has only 20 point modules and infinitely many fat point modules of multiplicity 2. The ring $B^{G,μ}$ falls under the purview of Artin and Stafford's classification of noncommutative curves, and we describe it using a sheaf of orders over an elliptic curve.

2016-01-14math.RA

关于任意域上上三角矩阵的星齐次分次多项式恒等式

On star-homogeneous-graded polynomial identities of upper triangular matrices over an arbitrary field

本文研究任意域上带精细群分次和齐次对合的上三角矩阵代数的分次多项式恒等式，给出基与渐近行为，并计算任意分次与对合下的指数和第二指数。

2024-02-05math.RA

Superrigidity from Chevalley groups into acylindrically hyperbolic groups via quasi-cocycles

We prove that every homomorphism from the elementary Chevalley group over a finitely generated unital commutative ring associated with reduced irreducible classical root system of rank at least 2, and ME analogues of such groups, into acylindrically hyperbolic groups has an absolutely elliptic image. This result provides a non-arithmetic generalization of homomorphism superrigidity of Farb--Kaimanovich--Masur and Bridson--Wade.

2018-01-26math.GRmath.GTmath.KT

涉及一对同次导出的函数恒等式及其在gr-素环中的中心值

Certain functional identities involving a pair of homogeneous derivations with central values in gr-prime rings

本文研究了gr-素环中涉及一对同次导出的函数恒等式，证明了在特定条件下环的交换性，并指出结果无法推广到gr-半素环。

2026-02-10math.RA

Division Algebras, Supersymmetry and Higher Gauge Theory

From the four normed division algebras--the real numbers, complex numbers, quaternions and octonions, of dimension k=1, 2, 4 and 8, respectively--a systematic procedure gives a 3-cocycle on the Poincare superalgebra in dimensions k+2=3, 4, 6 and 10, and a 4-cocycle on the Poincare superalgebra in dimensions k+3=4, 5, 7 and 11. The existence of these cocycles follow from spinor identities that hold only in these dimensions, and which are closely related to the existence of the superstring in dimensions k+2, and the super-2-brane in dimensions k+3. In general, an (n+1)-cocycle on a Lie superalge…

2011-06-17hep-thmath-phmath.DG

Hochschild上同调的同伦提升映射及其与使用约化系统的代数形变的联系

Homotopy lifting maps on Hochschild cohomology and connections to deformation of algebras using reduction systems

该研究利用同伦提升映射刻画Koszul箭图代数Hochschild上同调的Gerstenhaber括号结构，引入递推标量描述相关映射，并通过两种方法确定特定箭图代数的Maurer-Cartan元。

2023-08-24math.RA

具有均质反交换的分级代数与几乎多项式增长的变体

Graded algebras with homogeneous involution and varieties of almost polynomial growth

本文研究了具有均质反交换的G-分级代数中码度序列的行为，通过排除列表中的代数来表征多项式增长的变体，并提供了几乎多项式增长变体的分类。

2025-12-04math.RA

$\mathbb{Z}$-graded polynomial identities of the Grassmann algebra

Let $F$ be an infinite field of characteristic different from 2, and let $E$ be the Grassmann algebra of an infinite dimensional $F$-vector space $L$. In this paper we study the $\mathbb{Z}$-graded polynomial identities of $E$ with respect to certain $\mathbb{Z}$-grading such that the vector space $L$ is homogeneous in the grading. More precisely, we construct three types of $\mathbb{Z}$-gradings on $E$, denoted by $E^{\infty}$, $E^{k^\ast}$ and $E^{k}$, and we give the explicit form of the corresponding $\mathbb{Z}$-graded polynomial identities. We show that the homogeneous superalgebras $E_{…

2020-08-28math.RA

Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras

Hom-Maltsev(-admissible) algebras are defined, and it is shown that Hom-alternative algebras are Hom-Maltsev-admissible. With a new definition of a Hom-Jordan algebra, it is shown that Hom-alternative algebras are Hom-Jordan-admissible. Hom-type generalizations of some well-known identities in alternative algebras, including the Moufang identities, are obtained.

2010-02-21math-phmath.MPmath.RA