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| Solvable quadratic Lie algebras | |
| 引用本文： | ZHU Linsheng Department of Mathematics,Changshu Institute of Technology,Changshu 215500,China. Solvable quadratic Lie algebras[J]. 中国科学A辑(英文版), 2006, 49(4): 477-493. DOI: 10.1007/s11425-006-0477-y |
| 作者姓名： | ZHU Linsheng Department of Mathematics Changshu Institute of Technology Changshu 215500 China |
| 作者单位： | ZHU Linsheng Department of Mathematics，Changshu Institute of Technology，Changshu 215500，China |
| 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. |
| 收稿时间： | 2004-09-01 |
| 修稿时间： | 2005-06-22 |
Solvable quadratic Lie algebras |
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| ZHU Linsheng. Solvable quadratic Lie algebras[J]. Science in China(Mathematics), 2006, 49(4): 477-493. DOI: 10.1007/s11425-006-0477-y | |
| Authors: | ZHU Linsheng |
| Affiliation: | Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China |
| Abstract: | 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. |
| Keywords: | solvable quadratic Lie algebra cohomlogy Cartan subalgebra |
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