The Betti Numbers for a Family of Solvable Lie Algebras

被引：0

作者：

Thanh Minh Duong ^{[1
]}

机构：

[1] Ho Chi Minh City Univ Pedag, Dept Phys, 280 An Duong Vuong, Ho Chi Minh City, Vietnam

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2017年 / 40卷 / 02期

关键词：

Quadratic Lie algebras; Solvable; Cohomology; Betti numbers; COHOMOLOGY;

D O I：

10.1007/s40840-017-0447-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a property of symplectic quadratic Lie algebras that their Lie algebra of inner derivations has an invertible derivation. A family of symplectic quadratic Lie algebras is introduced to illustrate this situation. Finally, we calculate explicitly the Betti numbers of a family of solvable Lie algebras in two ways: using the cohomology of quadratic Lie algebras and applying a Pouseele's result on extensions of the one-dimensional Lie algebra by Heisenberg Lie algebras.

引用

页码：735 / 746

页数：12

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