(*)-serial Incidence代数(英文)

设K是一个代数闭域,A是域K上一个有限维代数.我们利用箭图方法给出了(*)-serial incidence代数的分类.     

关于Weyl模的连结同态

设 G 是特征数 p>0的代数闭域 K 上的单连通半单线性代数群.本文讨论了 Weyl 模的连结同态以及某类复合同态是非零的条件,推广了[3],[7]的有关结果.     

$M_{2}({\mathbb F})$上的$H$-模代数结构

设${\mathbb F}$是特征为零的代数闭域, $H$为非点化非幺模的8维非半单Hopf代数, $M_{2}({\mathbb F})$为${\mathbb F}$上二阶方阵组成的全矩阵代数. 本文的主要目的是讨论和分类$M_{2}({\mathbb F})$上所有的$H$-模代数结构.     

单扩张型Lie Rinehart代数的分类定理

定义单扩张型Lie Rinehart代数,从而给出一种通过导子构造Lie Rinehart代数的途径.指出这是一种特殊的作用Lie Rinehart代数.在系数环是没有零因子的交换代数的前提下,给出单扩张型Lie Rinehart代数的完全分类定理.特别的,证明多项式环上的任何非平凡作用Lie Rinehart代数必然是单扩张型的,并给出其标准型.     

低维幂零李代数的Yang-Baxter算子

在特征零的代数闭域F上,利用3维和4维幂零李代数的分类,通过计算刻画了3维和4维幂零李代数的Yang-Baxter算子.     

六维Heisenberg李超代数的Yang-Baxter方程

利用六维Heisenberg李超代数的分类,在特征0的代数闭域F上通过计算刻画了六维Heisenberg李超代数Yang-Baxter方程所有的解.     

交换代数上Zinbiel代数的钻石合成引理

先用非结合代数的合成运算给出域κ上Zinbiel代数的Grbner-Shirshov基和κ-线性基.然后证明自由交换代数κ[Y]上Zinbiel代数的钻石合成引理.     

一类对角非交换的三角代数

构造不变投影格仅含有两个非平凡投影且对角为非交换代数的三角代数, 并证明此三角代数的极大性.     

五维Heisenberg李超代数的Rota-Baxter算子

根据Heisenberg李超代数中心元的奇偶性的分类方法,通过计算刻画了特征零代数闭域F上五维Heisenberg李超代数η_(1,2)和η_2的所有Rota-Baxter算子.     

关于单李超三系的分类(英文)

本文证明了特征零代数闭域上的单李超三系可分为两部分:一是将单李超代数视为李超三系;二是单李超代数的对合自同构的(-1)-特征子空间.这些推广了Lister和Meyberg给出的关于单李三系分类的相应结果.     

Socle Deformations of Selfinjective Algebras of Euclidean Type

We classify all selfinjective finite dimensional algebras over an algebraically closed field which are socle equivalent to the selfinjective algebras of Euclidean type. In particular, nonstandard domestic selfinjective algebras in any characteristic of the base field are exhibited.     

Socle equivalences of weighted surface algebras

We describe the structure and properties of the finite-dimensional symmetric algebras over an algebraically closed field K which are socle equivalent to the general weighted surface algebras of triangulated surfaces, investigated in [11]. In particular, we prove that all these algebras are tame periodic algebras of period 4. The main results of this paper form an essential step towards a classification of all symmetric tame periodic algebras of period 4.     

A homological approach to representations of algebras II: tame hereditary algebras

We determine the pure global dimension of finite dimensional hereditary or radical-squared zero algebras over algebraically closed fields. The results are applied to algebras of dimension four and to the incidence algebras of critical ordered sets studied by Loupias. We further prove that the path algebra of an oriented cycle shares with Dedekind domains the Kulikov property (submodules of pure-projective modules are pure-projective).     

On the class equation for Hopf algebras

We give a simple proof of the Kac-Zhu class equation for semisimple Hopf algebras over an algebraically closed field of characteristic 0.

     

Derived Equivalence Classification of Nonstandard Selfinjective Algebras of Domestic Type

We give a complete derived equivalence classification of all nonstandard representation-infinite domestic selfinjective algebras over an algebraically closed field. As a consequence, a complete stable equivalence classification of these algebras is obtained.     

3-Lie bialgebras

3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of characteristic zero are provided.     

3-LIE BIALGEBRAS

3-Lie algebras have close relationships with many important fields in mathemat- ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char- acteristic zero are provided.     

Representations of Frobenius-type triangular matrix algebras

The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g., that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices.     

Central simple Poisson algebras

Poisson algebras are fundamental algebraic structures in physics and sym-plectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.