δ-BiHom-Jordan-李超代数的表示

本文研究δ-BiHom-Jordan-李超代数的表示.特别是详细地研究δ-BiHomJordan-李超代数的伴随表示、平凡表示、形变.作为应用,还讨论δ-BiHom-Jordan-李代数的导子.     

δ-Jordan李超代数的交换扩张

通过δ-Jordan李超代数T的表示和上同调理论,构造δ-Jordan李超代数T■V.证明了δ-Jordan李超代数的等价交换扩张给出相同的表示.通过δ-Jordan李超代数的表示和其交换扩张得到2-上圈.     

李超代数与Frobenius代数

利用限制李超代数的新定义,给出了李超代数的p-包络的一些相关结果,并将李代数中表示理论的一些结果推广到李超代数上,进而研究了限制李超代数与Frobenius代数的关系.     

李超代数与Frobenius代数

利用限制李超代数的新定义,给出了李超代数的p-包络的一些相关结果,并将李代数中表示理论的一些结果推广到李超代数上,进而研究了限制李超代数与Frobenius代数的关系．     

A(m,n)型余分裂李超代数

详细讨论了A(m,n)型余分裂李超代数的结构及其李超代数伴随表示,Killing型和李余超代数结构之间的关系.     

李超代数不可分解表示的Boson—Fermion实现

本文从普遍的代数观点出发,考虑到李超代数的Boson-Fermion实现,研究了任意李超代数在Heisenberg-Weyl超代数的通用包络代数相关空间上的无穷维不可分解表示。在特定的商空间上,这个表示将诱导出各种有限维表示,通常的不可约表示仅作为特殊情况给出。作为具体例子,我们给出了典型李超代数Gsl(2)(B(0,1),在耦合基下的不可分解表示。最后,我们证明了荷载这种无穷维不可分解表示的商空间同构于物理空间——广义Fock空间。     

着色李超代数与左着色对称结构

本文研究了着色李超代数上的左着色对称结构问题.利用着色李超代数的两种仿射表示和1-上同调群,得出左着色对称结构存在的几个充分或必要条件,推广了文[2]的结论.     

4阶特殊线性李超代数的型心与拟型心

主要研究了复数域上的特殊线性李超代数sl(m,n)的型心与拟型心,其中m+n=4.应用解线性方程组的方法,完全确定了这些李超代数型心和拟型心的矩阵表示.     

李超代数的Schur引理

对经典文献中李超代数的Schur引理的各种表述进行比对研究.给出李超代数的Schur引理的明晰表达及证明;作为应用,刻画了一类Heisenberg李超代数的不可约模的自同态.进而利用奇偶函子和符号映射刻画了李超代数模同态的各种定义之间的关系.     

扩张Hamilton李超代数的Borel子代数

设为特征零的代数闭域上秩为5的有限维Z-分次Hamilton单李超代数H通过添加次数导子得到的扩张李超代数.本文通过对正则元的分类,证明了关于典范环面共有160个正根系,从而得到160个Borel子代数;通过单根以及连接的定义,确定了每一个正根系的单根系,进而刻画了任意两个Borel子代数的连接关系;最后证明了共有48个Borel子代数是极大可解子代数.本文所得结果可用于进一步研究Cartan型单李超代数的结构与表示.     

Representations of Bihom-Lie superalgebras

The purpose of this article is to study cohomology and representations of Bihom-Lie superalgebras. In particular, trivial representations and adjoint representations of Bihom-Lie superalgebras are studied in detail. Derivations and central extensions of Bihom-Lie superalgebras are also discussed as an application.     

The abelian subalgebras of maximal dimensions for general linear Lie superalgebras

Over an algebraically closed field of characteristic zero, all the abelian subalgebras of maximal dimensions for the general linear Lie superalgebras are classified in the sense of conjugation. As a consequence, the minimal faithful representations are determined for the so-called nice abelian Lie superalgebras.     

δ-Hom-Jordan Lie superalgebras

This paper is primarily concerned with δ-Hom-Jordan Lie superalgebras. We discuss the concepts of α^k-derivations, representations and T*-extensions of δ-Hom-Jordan Lie superalgebras in detail, and some cohomological characterizations are established.     

Kostant homology formulas for oscillator modules of Lie superalgebras

We provide a systematic approach to obtain formulas for characters and Kostant u-homology groups of the oscillator modules of the finite-dimensional general linear and ortho-symplectic superalgebras, via Howe dualities for infinite-dimensional Lie algebras. Specializing these Lie superalgebras to Lie algebras, we recover, in a new way, formulas for Kostant homology groups of unitarizable highest weight representations of Hermitian symmetric pairs. In addition, two new reductive dual pairs related to the above-mentioned u-homology computation are worked out.     

Pointed representations of Virasoro algebra

In this paper we study the pointed representations of the Virasoro algebra. We show that unitary irreducible pointed representations of the Virasoro algebra are Harish-Chandra representations, thus they either are of highest or lowest weights or have all weight spaces of dimension 1. Further, we prove that unitary irreducible weight representations of Virasoro superalgebras are either of highest weights or of lowest weights, hence they are also Harish-Chandra representations. This work was supported by CNSF     

Minimal dimensions of faithful representations for abelian Lie superalgebras

This paper determines the minimal dimensions of faithful representations for abelian Lie superalgebras of finite dimensions over an algebraically closed field of characteristic zero. In particular, we also obtain the maximal dimensions of abelian subalgebras for the general linear Lie superalgebras.     

Representations of alternative algebras and superalgebras

This paper is a survey of results on representations of alternative algebras and superalgebras. In particular, new results of the authors on the subject are presented.     

Minimal faithful representations of abelian Jordan algebras and Lie superalgebras

Over an algebraically closed field of characteristic zero, all the abelian subalgebras of the maximal dimension are classified for any special Jordan algebra. As a consequence, the minimal dimension of the faithful representations of any finite-dimensional abelian Jordan algebra is determined and the minimal faithful representations are classified for the so-called nice abelian Jordan algebras. The same is done for the purely odd Lie superalgebras.     

Universal representations of Lie algebras by coderivations

A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincaré-Birkhoff-Witt theorem, extending this theorem to a class of nilpotent Lie superalgebras. Other applications are presented. Our results are new already for Lie algebras.