半格分次弱Hopf代数的$G$-Cleft扩张

本文首先将Clifford幺半群代数分解为交叉积的半格直和,然后将这个结果通过$H$-$G$-cleft扩张推广到所谓的$G$-交叉积上.     

一类Schrdinger-Virasoro型李代数的量子化

李双代数的量子化是获取新的量子群的重要方法.本文通过Drinfel'd扭元,对一类Schr(o|¨)dinger-Virasoro型李代数进行了量子化,得到了一类既非交换又非余交换的Hopf代数.     

4维幂零李代数的导子与triple导子

利用导子和triple导子的定义,刻画了特征不等于2的代数闭域上4维幂零李代数的导子和triple导子.     

图表追踪的一种机器实现方法

交换图表追踪法是同调代数中一种重要的证明方法.本文提出了一种基于前推的交换图表追踪的机器实现方法,它可以证明同调代数中一系列基于交换图的定理.该方法从定理的结论出发,通过构造辅助元素以及对辅助元素进行推导,能在有限步内给出定理的证明.本文提出的前推方法已经在Java开发平台上实现,同调代数中的五引理、九引理、蛇引理等的证明都可以由我们的程序自动产生.     

One-Point Extensions of t-Koszul Algebras

We introduce the category of t-fold modules which is a full subcategory of graded modules over a graded algebra. We show that this subcategory and hence the subcategory of t-Koszul modules are both closed under extensions and cokernels of monomorphisms. We study the one-point extension algebras, and a necessary and sufficient condition for such an algebra to be t-Koszul is given. We also consider the conditions such that the category of t-Koszul modules and the category of quadratic modules coincide.     

（2＋1）-DIMENSIONAL Tu HIERARCHY AND ITS INTEGRABLE COUPLINGS AS WELL AS THE MULTI-COMPONENT INTEGRABLE HIERARCHY

Under the frame of the(2 1)-dimensional zero curvature equation and Tu model,(2 1)-dimensional Tu hierarchy is obtained.Again by employing a subalgebra of the loop algebra ■_2 the integrable coupling system of the above hierarchy is presented.Finally,A multi-component integrable hierarchy is ob- tained by employing a multi-component loop algebra ■_M.     

L-Fuzzy代数的L-Fuzzy代数同态(英文)

本文研究了L-fuzzy代数的L-fuzzy代数同态的定义及其性质.利用L-fuzzy集的水平截集,得到TL-fuzzy代数的L-fuzzy代数同态的若干等价刻画.     

Actions of Ore extensions and growth of polynomial H-identities

We show that if A is a finite-dimensional associative H-module algebra for an arbitrary Hopf algebra H, then the proof of the analog of Amitsur’s conjecture for H-codimensions of A can be reduced to the case when A is H-simple. (Here we do not require that the Jacobson radical of A is an H-submodule.) As an application, we prove that if A is a finite-dimensional associative H-module algebra where H is a Hopf algebra H over a field of characteristic 0 such that H is constructed by an iterated Ore extension of a finite-dimensional semisimple Hopf algebra by skew-primitive elements (e.g., H is a Taft algebra), then there exists integer PIexp^H(A). In order to prove this, we study the structure of algebras simple with respect to an action of an Ore extension.     

On Ringel–Hall Algebras of Tame Hereditary Algebras

In this paper, the double Ringel–Hall algebras of tame hereditary algebras are decomposed as the quantized enveloping algebras of the infinite-dimensional Lie algebras, which are the central extensions of the affine loop algebras and the infinite-dimensional Heisenberg algebras. The numbers of the generators of the Heisenberg algebras are explicitly given at each dimensional level.