| Solvable quadratic Lie algebras |
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| 作者姓名： | ZHU Linsheng |
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| 作者单位： | ZHU Linsheng Department of Mathematics，Changshu Institute of Technology，Changshu 215500，China |
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| 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.
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| 收稿时间： | 1 September 2004 |
| 修稿时间： | 22 June 2005 |
Solvable quadratic Lie algebras |
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| ZHU Linsheng.Solvable quadratic Lie algebras[J].Science in China(Mathematics),2006,49(4):477-493. |
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| Authors: | ZHU Linsheng |
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| Institution: | Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China |
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| 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. |
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| Keywords: | solvable quadratic Lie algebra cohomlogy Cartan subalgebra |
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