Modules of the Intermediate Series over Not-finitely Graded Lie Algebras W(Γ)

Let W(Γ)be a class of not-finitely graded Lie algebras related to gener-alized Virasoro algebras with basis{Lα,i,C | α ∈ Γ,i ∈ Z+},which satisfies relations[Lα,i,Lβ,j]=(β-α)Lα+β,i+j+(j-i)Lα+β,i+j+1+δα+β,0δi+j,0α3-α/12C and[C,Lα,i]=0.In this paper,W(Γ)-modules of the intermediate series satisfying some conditions are con-structed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra.     

Quantizer–dequantizer operators as a tool for formulating the quantization procedure

We consider the quantization procedure and investigate the application of the quantizer–dequantizer method and star-product technique to construct associative products and the associative algebras formed by the quantizer–dequantizer operators and their symbols. The corresponding Lie algebras are also constructed. We study the case where the quantizer–dequantizer operators form a self-dual system and show that the structure constants of the Lie algebras satisfy some identity, in addition to the Jacobi identity. Using tomographic quantizer–dequantizer operators and their symbols, we construct the continuous associative algebra and the corresponding Lie algebra.     

Quantum R-matrices and factorization problems

A relation between quantum R-matrices and certain factorization problem in Hopf algebras is established. A definition of dressinf transformation in the quantum case is also given.     

环上的广义导子与Von Neumann代数上的P-核值保持映射

设Ａ是Ｂ（Ｈ）的子代数，ψ是Ａ到Ａ的线性映射，且对Ａ中的每个正交投影算子ｐ，有ψ（ｐ）（ｋｅｒｐ）ｒａｎｐ，则称ψ是Ａ到Ａ的Ｐ－核值保持映射，本文主要得到如下结果：每个２－非绕的半素环上的广义Ｊｏｒｄａｎ导子都是广义导子；每个ＶｏｎＮｅｕｍａｎｎ代数上的范数拓扑连续的Ｐ－核值保持映射是广义内导子．     

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.     

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.     

(*)-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.