Daoji Meng

The derivation algebra of the associative algebra C q [X,Y,X -1,Y -1] *

The derivation algebra Lof the associative algebra Cq[X,Y,X -1,Y -1] (q n :≠1,n∈ N)and the automorphism group Aut Lof L are given.

The Strong Semi-simple n-Lie Algebras

Abstract In this paper, we define the strong semi-simple n-Lie algebra, and prove: (1) A finite dimensional n-Lie algebra A over an algebraically closed field F of characteristic 0 is strong semi-simple if and only if A can be decomposed into the direct sum of its simple ideals. (2) Each derivation of a strong semi-simple n-Lie algebra is inner. (3) The Killing form on a strong semi-simple n-Lie algebra is nondegenerate, and other properties.

Complete Lie algebras

A remark on complete Lie algebras is given. Since the theory of complete Lie algebras is still developing, this remark cannot be complete.

The derivation algebra and the universal central extension of the q-analog of the virasoro-like algebra *

In this paper, the derivation algebra and the universal central extension of the q-analog of the Virasoro-like algebra are given.

The structures of bi-symmetric algebras and their sub-adjacent lie algebras

In this paper, we discuss the structures of bi-symmetric algebras and their sub-adjacent Lie algebras. We also give some results on their classification.

QUADRATIC LIE ALGEBRAS AND COMMUTATIVE ASSOCIATIVE ALGEBRAS

This paper is concerned with the tensor product ⊗ R of a quadratic Lie algebra and a commutative associative algebra R, the dimension of the space of invariant symmetric bilinear forms on a quadratic Lie algebra and a way to classify the quadratic Lie algebras. When is quadratic, some conditions are obtained such that ⊗ R is also quadratic and an optimistic lower bound for the dimensions of space invariant symmetric bilinear forms on a quadratic Lie algebra is given by means of their centers and Levi factors. At last, we give a way to classify the irreducible quadratic Lie algebras and realize a class of them by the tensor products of quadratic Lie algebras and commutative associative algebras.

The realization and structure of complete Lie algebras whose nilpotent radicals are Heisenberg algebras

The realization and siructure of complete Lie algebras whose nilpotent radicals are Heisenberg algebras over the complex field C are given.

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 Real Simple Left-symmetric Algebras

In this article, we commence to study the real (simple) left-symmetric algebras. From the known classification of certain complex (semi)simple left-symmetric algebras, we classify their corresponding real forms. We not only obtain the classification of real simple left-symmetric algebras in low dimensions, but also find certain examples of real simple left-symmetric algebras in higher dimensions. In particular, there exists a complex simple left-symmetric algebra without any real form. We also give a geometric construction for a class of real simple left-symmetric algebras. At last, we apply the classification results to study some structures related to geometry.

On bi-symmetric algebras

LEFT-symmetric algebra is a new kind of algebra system obtained from the studying of Lie al-gebra, Lie group and differential geometry. It is very useful for many topics in geometry andalgebra. In this note, we discuss a special kind of left-symmetric algebra which is verymeaningful--bi-symmetric algebra.