Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral <Emphasis Type="Italic">su</Emphasis>(2) WZNW Model

A zero modes’ Fock space is constructed for the extended chiral WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping algebra at an even root of unity, and of its infinite dimensional extension by the Lusztig operators We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations of A central result is the characterization of the Grothendieck ring of both and in Theorem 3.1. The properties of the fusion ring in are related to the braiding properties of correlation functions of primary fields of the conformal current algebra model.      

新型Poisson括号意义下的无穷维Lie代数

本文首先针对ＫｄＶ方程的Ｈａｍｉｌｔｏｎ形式，建立一种比较容易验证的新型Ｐｏｉｓｓｏｎ括号和无穷维Ｌｉｅ代数．其次，研究ＫｄＶ方程的Ｈａｍｉｌｔｏｎ形式的第一积分与新型Ｐｏｉｓｏｎ括号的关系，得到判定第一积分的充分必要条件．最后，构造ＫｄＶ方程的第一积分．     

Dm型正交代数的极大幂零子代数上保零李括积的映射

令F表示任意域,l_(2m)(F)表示F上D_m型正交李代数的极大幂零子代数.本文的目的是当m≥5时,刻画l_(2m)(F)上的每一个双向保零李括积的映射.利用文献[7]的主要结果和矩阵计算技巧,本文证明了l_(2m)(F)上的一个线性映射φ是双向保零李括积的当且仅当φ能够写成内自同构,图自同构,广义的对角自同构,中心映射,次中心自同构,极端映射和标量乘法的乘积.这推广了文献[7]的主要结果.     

严格循环的算子代数

设X是半自共轭的Banach空间,而A是B(X)的严格循环的交换子代数,考虑算子代数A的一些性质,这些性质与算子代数的自反性有关,而且这些性质为讨论A的自反性提供了理论基础.     

Batalin–Vilkovisky algebra structures on Hochschild cohomology of generalized Weyl algebras

We devote to the calculation of Batalin–Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi–Yau generalized Weyl algebras. We first establish a Van den Bergh duality at the level of complex. Then based on the results of Solotar et al., we apply Kowalzig and Krähmer's method to the Hochschild homology of generalized Weyl algebras, and translate the homological information into cohomological one by virtue of the Van den Bergh duality, obtaining the desired Batalin–Vilkovisky algebra structures. Finally, we apply our results to quantum weighted projective lines and Podleś quantum spheres, and the Batalin–Vilkovisky algebra structures for them are described completely.     

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.     

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.