Simple Lie Algebras and Complete Lie Algebras

ＳｉｍｐｌｅＬｉｅＡｌｇｅｂｒａｓａｎｄＣｏｍｐｌｅｔｅＬｉｅＡｌｇｅｂｒａｓ＊）ＹａｎｇＱｉ（杨奇）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙ，Ｔｉａｎｊｉｎ，３０００７２）ＭｅｎｇＤａｏｊｉ（孟道骥）（Ｄ...     

Lie余模和Lie双代数的构造

首先给出Lie余模的直和分解, 然后根据Lie余模理论由Lie余代数构造某些(三角)Lie双代数.     

Lie comodules and the constructions of Lie bialgebras

In this paper,we first give a direct sum decomposition of Lie comodules,and then accord- ing to the Lie comodule theory,construct some(triangular)Lie bialgebras through Lie coalgebras.     

On an Isospectral Lie–Poisson System and Its Lie Algebra

In this paper we analyze the matrix differential system X' = [N,X²], where N is skew-symmetric and X(0) is symmetric. We prove that it is isospectral and that it is endowed with a Poisson structure, and we discuss its invariants and Casimirs. Formulation of the Poisson problem in a Lie-Poisson setting, as a flow on a dual of a Lie algebra, requires a computation of its faithful representation. Although the existence of a faithful representation, assured by the Ado theorem and a symbolic algorithm, due to de Graaf, exists for the general computation of faithful representations of Lie algebras, the practical problem of forming a "tight" representation, convenient for subsequent analytic and numerical work, belongs to numerical algebra. We solve it for the Poisson structure corresponding to the equation X' = [N,X²].     

Hamiltonian type Lie bialgebras

We first prove that,for any generalized Hamiltonian type Lie algebra H,the first co- homology group H~1(H,H(?)H) is trivial.We then show that all Lie bialgebra structures on H are triangular.     

Lie Bialgebras of a Family of Lie Algebras of Block Type

Lie bialgebra structures on a family of Lie algebras of Block type are shown to be triangular coboundary.     

完备Lie超代数

本文引入了完备Ｌｉｅ超代数和Ｌｉｅ超代数的全形这两个概念，讨论了完备Ｌｉｅ超代数的一些等价条件和结构定理。所得结果是Ｊａｃｏｂｓｏ［１］和ＮｅｎｇＤａｏｊｉ［２］的推广。     

Solvable quadratic Lie algebras

A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.     

Characteristic Semi-simple Lie Algebras and Completely Semi-simple Lie Algebras over any Field

In this paper, we study some properties of the finite dimensional characteristic semi-simple (C.S.S.) Lie algebras and completely semi-simple Lie algebras over any field. The definitions and some results of these algebras have been given by G.B.Seligman in [1]. We can easily prove the following lemmas: Lemma 1 The centre of any finite dimensional Lie algebra L is a characteristic ideal of L.     

形式向量场的一般Lie超代数与特殊Lie超代数

证明了形式向量场的一般Lie超代数W与特殊Lie超代数S的自然滤过是不变的.进而证明了W与S的自同构群同构于它们的底代数U的可许自同构群,于是W与S的自同构都是由U的连续自同构所诱导的.     

A-扩张Lie Rinehart代数

The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative,associative algebra A.It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group,analogous to the well known relationship of Lie algebras and Lie groups.     

Modular Lie Superalgebras of H-type

In this article the Z-graded transitive modular Lie superalgebra -1 Li,whose repre-sentation of L_0 in L_(-1) is isomorphic to the natural representation of osp(L_(-1)),is determined.     

互补可换Lie代数

若L是有限维非幂零Lie代数,J（L）＝∞／∩／i=1L^i,称为互补可换Lie代数,如果J（L）与L的Cartan子代数是可换的,且L的每一真理想均包含J（L）。本完全刻划了代数闭域与实数域上互补可换Lie代数的特征。     

Lie超代数及二次Lie超代数的分解惟一性

一个带有非退化超对称不变双线性型的Lie超代数称为二次Lie超代数. 考虑Lie超代数的分解, 得到在同构意义下一个Lie超代数分解为不可分解阶化理想直和的方式惟一及在保距同构意义下一个二次Lie超代数分解为不可约非退化阶化理想直和的方式惟一.     

Infinite Rank Affine Lie Algebras

１．ＩｎｆｉｎｉｔｅＲａｎｋＡｆｉｎｅＬｉｅＡｌｇｅｂｒａｓｇ（Ｘ）ａｎｄｇ（Ｘ）ＷｅｒｅｃａｌｔｈｅｄｅｆｉｎｉｔｉｏｎｏｆｉｎｆｉｎｉｔｅｒａｎｋａｆｉｎｅＬｉｅａｌｇｅｂｒａｓａｎｄｔｈｅｉｒｆｕｎｄａｍｅｎｔａｌｓｔｒｕｃｔｕｒｅ．Ａｇｅｎｅ...     

Global Lie–Tresse theorem

We prove a global algebraic version of the Lie–Tresse theorem which states that the algebra of differential invariants of an algebraic pseudogroup action on a differential equation is generated by a finite number of rational-polynomial differential invariants and invariant derivations.     

广义Hamilton Lie双代数

首先证明,对于任意广义Hamilton Lie 代数H, 一阶上同调群H1( H, H H)是平凡的. 其次证明H上的 所有Lie双代数结构是上三角的.     

单的完备Lie代数

给出了一个Ｈｅｉｓｅｎｂｅｒｇ代数与一个交换Ｌｉｅ代数的直和ｇ０的全形ｈ（ｇ０）和ｈ（ｇ０）的导子代数Ｄｅｒｈ（ｇ０）．证明了ｈ（ｇ０）不是一个完备Ｌｉｅ代数，但Ｄｅｒｈ（ｇ０）是一个单完备Ｌｉｅ代数．