李超代数sl_(2|1)到Kac模的一次上同调

在特征P3的域上,首先对李超代数sl_(2/1)的一类Kac模进行权空间分解,然后计算sl_(2/1)到其Kac模的权导子,进而决定了sl_(2/1)到该Kac模的一次上同调.     

系数在模李超代数W(m,3,1)上的gl(2,F)的一维上同调

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

模切触超代数偶部到奇部的导子(英文)

本文研究了K模Wˉ1中K的非负偶次数的1上圈问题.利用计算导子在其生成元上作用,获得了简约定理和K模W1ˉ中K的非负偶次数的1上圈,推广了模切触超代数偶部导子.     

Cartan型模李超代数W的二阶上同调群H2(W,F)

本文研究了有限维广义Witt李超代数W的二阶上同调群H2(W,F),其中F是一个特征P＞2的代数封闭域.通过计算W到W*的导子,得到H2(W,F)是平凡的.应用此结果,我们可得W的中心扩张是平凡的.     

有限秩算子的表示(Ⅰ)

定义了子空间格代数的(弱闭双边)模,对有限维Hilbert空间的强自反子空间格代数的模及原子Boolean格代数的模中的有限秩算子进行了讨论,得到有限秩算子一定可以表示为秩1算子的和.     

李超代数gl_(2|1)到Witt超代数的低维上同调

Witt超代数在伴随表示的意义下是一般线性李超代数gl_(2|1^-)模.通过对Witt超代数进行子模分解和权空间分解,用简约的方法计算了gl_(2|1-)模.通过对Witt超代数进行子模分解和权空间分解,用简约的方法计算了gl_(2|1^-)到Witt超代数的低维上同调.     

有限维单Cartan型模李超代数HO

本文构造了一族有限维Cartan型模李超代数-奇Hamilton模李超代数HO, 并证明了其单性.通过建立Cartan型模李超代数W,H,K,S和HO的维数公式,讨 论了奇Hamilton模李超代数HO与Cartan型模李超代数W,S,H,K的同构关系.     

无限维奇Hamilton模李超代数的导子

本文首先确定了无限维奇Hamilton模李超代数的生成元集,然后确定了奇Hamilton模李超代数到广义Witt模李超代数的导子空间,进而确定了无限维奇Hamilton模李超代数的导子代数.     

半单代数群的FROBENIUS核的主不可分解模的滤过

设 G 是特征数 p>0的代数闭域 K 上单连通半单代数群.笔者在[5]中讨论了 G 的第n 个(n 是任意自然数)Frobenius 核的超代数 u_(?) 的主不可分解模 Q(λ,n)的以 Weyl 模为子商的 G-模滤过——Weyl 滤过.证明了当 p≥2h-2时,Q(λ,n)(?)V(v)~(p~n)有一个Weyl 滤过;对每个λ∈X_n,定义了一个集合     

L(V)是无限维中心代数的初等证明

研究域F上无限维线性空间V的任一子空间W的线性变换在V上的扩张,用初等方法可证明V的线性变换代数L(V)是无限维的中心代数.在一定意义上推广了域F上的n级矩阵代数是中心代数这一结果.     

Dual Lie Bialgebra Structures of W -algebra W (2, 2) Type

In the present paper, we investigate the dual Lie coalgebras of the centerless W(2, 2) algebra by studying the maximal good subspaces. Based on this, we construct the dual Lie bialgebra structures of the centerless W(2, 2) Lie bialgebra. As by-products, four new infinite dimensional Lie algebras are obtained.     

Characters of Representations for Lie Superalgebras of Type C Using Tableaux

Let  = osp(2, 2n) denote the complex Lie superalgebra of type C of rank n + 1. Let V(λ) denote the irreducible representation of  with the highest weight λ. For each finite dimensional V(λ), we describe the character of V(λ) combinatorially using the generalized osp(2, 2n)-standard tableaux of λ.     

Generalized Schur-concave Functions and Eaton Triples

Motivated by Schur-concavity, we introduce the notion of G -concavity where G is a closed subgroup of the orthogonal group O ( V ) on a finite dimensional real inner product space V . The triple ( V , G , F ) is an Eaton triple if F ² V is a nonempty closed convex cone such that (A1) Gx 7 F is nonempty for each x ε V . (A2) max g ε G ( x,gy ) = ( x,gy ) for all x, y ε F . If W := span F and H := { g | W : g ε G , gW = W } ² O ( W ), and ( W , H , F ) is an Eaton triple, then ( W , H , F ) is called a reduced triple of the Eaton triple ( V , G , F ). In this event, a characterization of the G -concavity in terms of H -concavity is obtained. Some differential characterizations of G -concavity are then given. The results are applied to Lie groups. Various matrix examples are given.     

Lie algebras of infinitesimal norm isometries

Given a norm on a finite dimensional vector space V, we may consider the group of all linear automorphisms which preserve it. The Lie algebra of this group is a Lie subalgebra of the endomorphism algebra of V having two properties: (1) it is the Lie algebra of a compact subgroup, and (2) it is “saturated” in a sence made precise below. We show that any Lie subalgebra satisfying these conditions is the Lie algebra of the group of linear automorphisms preserving some norm. There is an appendix on elementary Lie group theory.     

粗糙核多线性分数次积分算子在Morrey-Herz空间中的有界性

研究两类带粗糙核的多线性分数次积分算子,用转化为相应的截断算子来研究的方法,得出它们是从M（K）α,λp1,q1）空间到M（K）α,λp1,q1）空上的有界算子,把前人Herz空间此类算子的有界性推广到Herz-Morrey空间.     

On Simple Split Lie Triple Systems

It is shown that simple split Lie triple systems with a coherent 0-root space and satisfying finiteness conditions are isomorphic to a direct limit of (well-known) finite dimensional simple Lie triple systems of a same type. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems.     

Stratonovich-Weyl correspondence for compact semisimple Lie groups

Let G be a compact Lie group, M a G-homogeneous space and π a unitary representation of G realized on a Hilbert space of functions on M. We give a general presentation of the Stratonovich-Weyl correspondence associated with π. In the case when G is a compact semisimple Lie group and π _λ an irreducible representation of G with highest weight λ, we study the Stratonovich-Weyl symbol of the derived operator d π _λ (X) for X in the Lie algebra of G and its behavior as λ goes to infinity.     

Generalized tangent representations for groups and symmetric spaces of matrices

Any two representations of dimensions n resp. r of a given group G allow the construction of a third representation φ in the space of rectangular n × r matrices K^n,r over the same ground field K. The φ-semidirect product of K^n,r and G then has (n + r) dimensional representation. The inhomogenizations of G and in case of matrix Lie groups G the tangent groups are special cases of this construction. The contragredient as well as the Lie algebraical versions of these results are included. In the final section the construction is generalized to symmetric spaces and their local algebraical structures, the Lie triples, by defining semidirect products resp. semidirect sums with respect to a representation