一类特征单的n-李代数

利用结合代数与n-李代数的张量积构造了一类无限维特征单的n-李代数,且证明了除n=3的情形以外,这类特征单n-李代数的内导子代数是特征单李代数.     

一类特征单的n-李代数

利用结合代数与n-李代数的张量积构造了一类无限维特征单的m-李代数,且证明了除n=3的情形以外,这类特征单n-李代数的内导子代数足特征单李代数.     

一类Heisenberg n-李代数的自同构群(英文)

本文主要研究Heisenberg n-李代数的结构.给出了一类(3m+1)-维Heisenberg3-李代数及(nm+1)-维Heisenberg n-李代数的自同构群.且给出了自同构的具体表达式.     

n-李代数的中心扩张

对n-李代数的中心扩张问题进行了研究,提出了Heisenberg n-李代数的概念,并对任意一个线性空间V,给出了构造Heisenberg n-李代数H(V)的一种方法且研究了一类特殊类型Heisenberberg n-李代数的导子代数的结构.     

(n-1)-半单的n-李代数的几何描述

证明了实数域上(n-1)-半单的(n+1)维n-李代数A是n维欧氏空间的Lorentz群O(p,n-p)与n维Abel正规子群的半直积的n-李代数.且当p=0时,A是n维欧氏空间的等距变换群的n-李代数.并提出了关于(n-1)-半单的(n+1)维n-李代数的外导子的物理应用与几何应用问题.     

最简线状n-李代数

定义了一类特殊的幂零n-李代数,即最简线状n-李代数,它是最简线状李代数的推广.确定了m维最简线状n-李代数A的导子代数Der(A)和自同构群Aut(A),定义了n-李代数的全形h(A)=Der(A)( ) A,并证明了当A的基域F的特征P为零或P＞m-n时,Der(A)是不可解的完备李代数,而h(A)的一个子代数是可解的完备李代数,当F的特征为零时,Aut(A)是无中心的不可解群.     

n-李代数的结构

主要研究特征为2的代数闭域上(n+1)维n-李代数的结构,给出了(n+1)维n-李代数的分类,描述了其可解性与幂零性,刻画了(n+1)维n-李代数的导子代数与内导子代数的结构.     

φ-自由n-李代数的结构

对φ-自由n-李代数的结构进行了研究,得到了特征零域上φ-自由伽李代数的分类定理及Levi 分解定理,同时也得到了任意域上n-李代数可解的等价条件.     

n-李代数的结构

主要研究特征为2的代数闭域上(n+1)维n-李代数的结构,给出了(n+1)维n-李代数的分类,描述了其可解性与幂零性,刻画了(n+1)维n-李代数的导子代数与内导子代数的结构.     

强半单的n-李代数的表示

本文主要研究了强半单的n-李代数的表示,证明了强半单的n-李代数的表示(V,ρ)可转化为一个约化李代数Lρ(V)的表示,并证明了不变线性形等其它相关性质．     

3-Filiform Leibniz algebras of maximum length,whose naturally graded algebras are Lie algebras

In this article we present the classification of the 3-filiform Leibniz algebras of maximum length, whose associated naturally graded algebras are Lie algebras. Our main tools are a previous existence result by Cabezas and Pastor [J.M. Cabezas and E. Pastor, Naturally graded p-filiform Lie algebras in arbitrary finite dimension, J. Lie Theory 15 (2005), pp. 379–391] and the construction of appropriate homogeneous bases in the connected gradation considered. This is a continuation of the work done in Ref. [J.M. Cabezas, L.M. Camacho, and I.M. Rodríguez, On filiform and 2-filiform Leibniz algebras of maximum length, J. Lie Theory 18 (2008), pp. 335–350].     

Quasi L 3 -Filiform Lie Algebras

Abstract

In this paper, we mainly discuss some properties of quasi L ₃-filiform Lie algebras and their derivation algebras.     

ON LIE ALGEBRAS WHOSE NILRADICAL IS (n — p)-FILIFORM

We prove first that every (n — p)-filiform Lie algebra, p ≤ 3, is the nilradical of a solvable, nonnilpotent rigid Lie algebra. We also analize how this result extends to (n — 4)-filiform Lie algebras. For this purpose, we give a classificaction of these algebras and then determine which of the obtained classes appear as the nilradical of a rigid algebra.     

The Classification of Naturally Graded p-Filiform Leibniz Algebras

In the present article the classification of n-dimensional naturally graded p-filiform (1 ≤ p ≤ n ? 4) Leibniz algebras is obtained. A splitting of the set of naturally graded Leibniz algebras into the families of Lie and non Lie Leibniz algebras by means of characteristic sequences (isomorphism invariants) is proved.     

ON 2-ABELIAN (n – 5)-FILIFORM LIE ALGEBRAS

We classify the (n ? 5)-filiform Lie algebras which have the additional property of a non-abelian derived subalgebra. Moreover we show that if a (n ? 5)-filiform Lie algebra is characteristically nilpotent, then it must be 2-abelian.     

A class of nilpotent lie algebras

A p-filiform Lie algebra g is a nilpotent Lie algebra for which Goze’s invariant is (n–p,1,…,1). These Lie algebras are well known for P ≥ n-4n = dim(g). In this paper we describe the p-filiform Lie algebras, for p = n-5 and we gjive their classification when the derived subalgebra is maximal.     

三次可解型非退化李代数及其导子李代数的结构

本文给出了非退化可解李代数的两个类型:三次可解型非退化李代数和扩充的 Heisenberg李代数,并确定三次可解型非退化李代数及其导子李代数的结构．     

关于局部顶点李代数的一些注记

本文研究局部顶点李代数与顶点代数之间的关系.利用由局部顶点李代数构造顶点代数的方法,定义局部顶点李代数之间的同态,证明了同态可以唯一诱导出由局部顶点李代数构造所得到的顶点代数之间的同态.     

The Jordan socle and finitary Lie algebras

In this paper we introduce the notion of Jordan socle for nondegenerate Lie algebras, which extends the definition of socle given in [A. Fernández López et al., 3-Graded Lie algebras with Jordan finiteness conditions, Comm. Algebra, in press] for 3-graded Lie algebras. Any nondegenerate Lie algebra with essential Jordan socle is an essential subdirect product of strongly prime ones having nonzero Jordan socle. These last algebras are described, up to exceptional cases, in terms of simple Lie algebras of finite rank operators and their algebras of derivations. When working with Lie algebras which are infinite dimensional over an algebraically closed field of characteristic 0, the exceptions disappear and the algebras of derivations are computed.     

Generalized Lie Algebras and Cocycle Twists

We use the results of Etingof and Gelaki on the classification of (co)triangular Hopf algebras to extend Scheunert's “discoloration” technique to Lie algebras in the category of (co)modules. As an application, we prove a PBW-type theorem for such Lie algebras. We also discuss the relationship between Lie algebras in the category of (co)modules and symmetric braided Lie algebras introduced by Gurevich. Finally, we construct examples of symmetric braided Lie algebras that are essentially different from Lie coloralgebras.