q-类似Virasoro-like代数模的导子

记Lq为两个变量的量子环面上的斜导子李代数,当0≠q∈C为非单位时,Lq就是q-类似Virasoro-like代数.本文给出了文中构造的Lq的模上的导子及一上同调群H^1（Lq,M）.     

广义扭Schr\"{o}dinger-Virasoro李代数的导子和2-上同调

通过计算,得到了广义扭Schr\"{o}dinger-Virasoro李代数的导子代数和2-上同调群.     

Graded Modules Over the q-Analog Virasoro-Like Algebra

In this paper, we deal with the classification of the irreducible Z-graded and Z ²-graded modules with finite dimensional homogeneous subspaces for the q analog Virasoro-like algebra L. We first prove that a Z-graded L-module must be a uniformly bounded module or a generalized highest weight module. Then we show that an irreducible generalized highest weight Z-graded module with finite dimensional homogeneous subspaces must be a highest (or lowest) weight module and give a necessary and sufficient condition for such a module with finite dimensional homogeneous subspaces. We use the Z-graded modules to construct a class of Z ²-graded irreducible generalized highest weight modules with finite dimensional homogeneous subspaces. Finally, we classify the Z ²-graded L-modules. We first prove that a Z ²-graded module must be either a uniformly bounded module or a generalized highest weight module. Then we prove that an irreducible nontrivial Z ²-graded module with finite dimensional homogeneous subspaces must be isomorphic to a module constructed as above. As a consequence, we also classify the irreducible Z-graded modules and the irreducible Z ²-graded modules with finite dimensional homogeneous subspaces and center acting nontrivial. Supported by the National Science Foundation of China (No 10671160), the China Postdoctoral Science Foundation (No. 20060390693), the Specialized Research fund for the Doctoral Program of Higher Education (No.20060384002), and the New Century Talents Supported Program from the Education Department of Fujian Province.     

First cohomology group of rank two Witt algebra to its Larsson modules

Let U = ℂ², Γ = ℤ², and let ℂ[x ₁^±1, x ₂^±1] be the ring of Laurent polynomials. The Witt algebra L is the Lie algebra of derivations over ℂ[x ₁^±1, x ₂^±1], which is spanned by elements of the form D(u, r) = x ^r (u ₁ d ₁ + u ₂ d ₂), u = (u ₁, u ₂) ∈ U, r ∈ Γ, where d ₁ and d ₂ are the degree derivations of ℂ[x ₁^±1, x ₂^±1]. The image of gl ₂-module V under Larsson functor F ^α , denoted by W = F ^α (V), gives a class of L-modules, often called the Larsson-modules of L. In this paper, we study the derivations from the Witt algebra L to its Larsson-modules W, and we determine the first cohomology group H ¹(L,W).     

Mod p Cohomology Algebra of Special Linear Group

Abstract

We shall calculate the mod p cohomology algebra of the special linear groups SL(3, F _p ) by analyzing the Carlson module of a regular cohomology class belonging to a system of parameters.     

Fibonacci代数平凡扩张的一阶Hochschild上同调群

基于Cibils等人对单项式代数的向量空间Alt(DΛ)的组合描绘,得到了Fibonacci代数平凡扩张的一阶Hochschild上同调群的维数.     

On the First Hochschild Cohomology linebreak of Admissible Algebras

The aim of this paper is to investigate the first Hochschild cohomology of admissible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators on an admissible algebra. Firstly, differential operators from a path algebra to its quotient algebra as an admissible algebra are discussed. Based on this discussion, the first cohomology with admissible algebras as coefficient modules is characterized, including their dimension formula. Besides, for planar quivers, the $k$-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field $k$ of characteristic $0$.     

系数在模李超代数~$W(m,3,\underline{1})$ 上的~$\frak{gl}(2,\mathbb{F})$ 的一维上同调

研究了系数在模李超代数~$W(m,3,\underline{1})$ 上的~$\frak{gl}(2,\mathbb{F})$ 的一维上同调, 其中~$\mathbb{F}$ 是一个素特征的代数闭域且~$\frak{gl}(2,\mathbb{F})$ 是系数在~$\mathbb{F}$ 上的~$2\times 2$ 阶矩阵李代数. 计算出所有~$\frak{gl}(2,\mathbb{F})$ 到模李超代数~$W(m,3,\underline{1})$ 的子模的导子和内导子. 从而一维上同调~$\textrm{H}^{1}(\frak{gl}(2,\mathbb{F}),W(m,3,\underline{1}))$ 可以完全用矩阵的形式表示.     

A Gap Cohomology Group

Dan Talayco has recently defined the gap cohomology group of a tower in p(ω)/fin of height ω₁. This group is isomorphic to the collection of gaps in the tower modulo the equivalence relation given by two gaps being equivalent (cohomologous) if their levelwise symmetric difference is not a gap in the tower, the group operation being levelwise symmetric difference. Talayco showed that the size of this group is always at least 2^N0 and that it attains its greatest possible size, 2^N1, if ? holds and also in some generic extensions in which CH fails, for example on adding many Cohen or random reals. In this paper it is shown that there is always some tower whose gap cohomology group has size 2^N1. It is still open as to whether there are models in which there are towers whose gap cohomology group has size less than 2^ω1.     

系数在基本Harish—Chandra模中的Virasoro代数的上同调群

设ｇ为特征为０的二次闭域上的Ｖｉｒａｓｏｒｏ代数。本文决定了Ｈ＾１（ｇ，Ｍ（４，１）），Ｈ＾２（ｇ，Ｍ（４，２））及Ｈ＾２（ｇ，ＭＬ）的结构，其中Ｍ（４，１），Ｍ（４，２）为两类基本Ｈａｒｉｓｈ－Ｃｈａｎｄｒａ模，ＭＬ为无常数项单变量Ｌａｕｒｅｎｔ多项式。     

The Partition Algebra as a Centralizer Algebra of the Alternating Group

ABSTRACT

In this article, we focus on the result of V.F.R. Jones which says that the partition algebra is the algebra of all transformations commuting with the action of the symmetric group on tensor products of its permutation representation. In particular, we restrict the action of the symmetric group to the action of the alternating group. In this context, we compute a basis for the centralizer algebra and show when the centralizer is isomorphic to the partition algebra.     

Virasoro—相似代数的导子代数

本文给出了Ｖｒａｓｏｒｏ－相似 代数的导子代数及导子代的自同构群。     

On the Structure of the Units of Group Algebra of Dihedral Group

In this paper, we completely determine the structure of the unit group of the group algebra of some dihedral groups D2 n over the finite field Fpk, where p is a prime.     

F[x,y] as a Dialgebra and a Leibniz Algebra

In this article, we define a new associative dialgebra over a polynomial algebra F[x, y] with two indeterminates x and y. Left derivations, right derivations, derivations, and automorphisms of F[x, y] as associative dialgebra are determined. Meanwhile, we also determine all homogeneous derivations of F[x, y] as ?-graded Leibniz algebra, and automorphisms of Leibniz algebra F[x, y] preserving the standard filtration.     

On the Generalized Enveloping Algebra of a Color Lie Algebra

Let G be an abelian group, ε an anti-bicharacter of G and L a G-graded ε Lie algebra (color Lie algebra) over a field of characteristic zero. We prove that for all G-graded, positively filtered A such that the associated graded algebra is isomorphic to the G-graded ε-symmetric algebra S(L), there is a G- graded ε-Lie algebra L and a G-graded scalar two cocycle , such that A is isomorphic to U _ω (L) the generalized enveloping algebra of L associated with ω. We also prove there is an isomorphism of graded spaces between the Hochschild cohomology of the generalized universal enveloping algebra U(L) and the generalized cohomology of the color Lie algebra L. Supported by the EC project Liegrits MCRTN 505078.     

Deformations on the Twisted Heisenberg-Virasoro Algebra

With the cohomology results on the Virasoro algebra, the authors determine the second cohomology group on the twisted Heisenberg-Virasoro algebra, which gives all deformations on the twisted Heisenberg-Virasoro algebra.     

On Derivations of the Ternary Malcev Algebra M 8

Derivations of the simple ternary Malcev algebra M ₈ and its algebra of multiplications are described.     

Mod 7 Cohomology Algebra of Held Simple Group

We calculate the mod7 cohomology algebra of the Held simple group, whose Sylow 7-subgroups are extraspecial of order 7³ and exponent 7. Our method depends on the analysis of the Carlson module of a regular class belonging to a system of parameters.