Solvable quadratic Lie algebras  

作　　者：ZHU Linsheng 

机构地区：[1]Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China

出　　处：《Science China Mathematics》2006年第4期477-493,共17页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10571119);the Natural Science Funds from Morningside Center of Mathematics,Chinese Academy of Sciences;the Eduction Department of Jiangsu Province.

摘　　要：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.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.

关 键 词：SOLVABLE QUADRATIC LIE algebra  cohomlogy  CARTAN subalgebra. 

分 类 号：N[自然科学总论]