COHOMOLOGY OF SOME FAMILIES OFLIE ALGEBRAS AND QUADRATIC LIEALGEBRAS

Abstract

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 [5]. This class contains Heisenberg Lie
algebras. In 1983, L. J. Santharoubane [11] 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 [6] 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