Cohomology of some families of Lie algebras and quadratic Lie algebras
| Autor: | Hai, Cao Tran Tu, Thanh, Duong Minh, Vu, Le Anh |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The paper studies the cohomology of Lie algebras and quadratic Lie algebras. Firstly, we propose to describe the cohomology of $MD(n,1)$-class which was introduced in \cite{LHNCN16}. This class contains Heisenberg Lie algebras. In 1983, L. J. Santharoubane \cite{San83} computed the cohomology of Heisenberg Lie algebras. In this paper, we will completely describe the cohomology of the other ones of $MD(n, 1)$-class. Finally, we will be concerned about the cohomology of quadratic Lie algebras. In 1985, A. Medina and P. Revoy \cite{MR85} computed the second Betti number of the generalized real diamond Lie algebras. We will compute in this paper the second Betti number of the generalized complex diamond Lie algebras by using the super-Poisson bracket. Comment: 18 pages, no figures |
| Databáze: | arXiv |
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