5维幂零李代数的导子代数的结构

对维数为5的所有幂零李代数的导子代数进行了研究,按照其分类分别给出了9种互不同构的导子代数的结构。     

On the Derivations of Filiform Leibniz Algebras

The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 733–742.Original Russian Text Copyright ©2005 by B. A. Omirov.     

Omni-Representations of Leibniz Algebras

In this paper,first we introduce the notion of an omni-representation of a Leibniz algebra g on a vector space V as a Leibniz algebra homomor-phism from g to the omni-Lie algebra gl(V)⊕ V.Then we introduce the omni-cohomology theory associated to omni-representations and establish the re-lation between omni-cohomology groups and Loday-Pirashvili cohomology groups.     

Cohomologies of Leibniz Algebras with Higher Derivations北大核心CSCD

本文研究具有高阶导子的莱布尼兹代数.我们称之为LeibHDer对.首先给出LeibHDer对的表示并构造半直积.最后,定义LeibHDer对的上同调并研究其中心扩张和形变理论.     

TUHF代数上的Lie导子

证明了TUHF代数丁上的Lie导子L形如D l．其中D是T上的结合导子，l是从T到它的中心Z上的线性映射且零化T中的括积．     

Toroidal李代数上的Poisson代数结构

非交换的Poisson代数同时具有结合代数和李代数两种代数结构,而结合代数和李代数之间满足所谓的Leibniz法则．文中确定了Toroidal李代数上所有的Poisson代数结构,推广了仿射Kac-Moody代数上相应的结论．     

Two Kinds of Solvable Complete Lie Algebras

In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nilpotent Lie algebras.     

Lie Higher Derivations on Nest Algebras

Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = （Ln）n∈N is a Lie higher derivation of AlgAl if and only if each Ln has the form Ln（A） ： Tn（A） ＋ hn（A）I for all A ∈ AlgN, where （Tn）n∈N is a higher derivation and （hn）n∈N is a sequence of additive functionals satisfying hn（[A,B]） = 0 for all A,B ∈ AlgN and all n ∈ N.     

Betti Number Behavior for Nilpotent Lie Algebras

We discuss three general problems concerning the cohomology of a (real or complex) nilpotent Lie algebra: first of all, determining the Betti numbers exactly; second, determining the distribution these Betti numbers follow; and finally, estimating the size of the individual cohomology spaces or the total cohomology space. We show how spectral sequence arguments can contribute to a solution in a concrete setting. For one-dimensional extensions of a Heisenberg algebra, we determine the Betti numbers exactly. We then show that some families in this class have a M-shaped Betti number distribution, and construct the first examples with an even more exotic Betti number distribution. Finally, we discuss the construction of (co)homology classes for split metabelian Lie algebras, thus proving the Toral Rank Conjecture for this class of algebras.     

4维幂零李代数的导子与triple导子

利用导子和triple导子的定义,刻画了特征不等于2的代数闭域上4维幂零李代数的导子和triple导子.