On the cohomology of frobeniusian model Lie algebras

Abstract

We compute the first and second cohomology groups with coefficients in the adjoint module of frobeniusian model algebras whose parameters move in a dense open subset of ${\mathbb{C}}^{p-1}$, and obtain upper bounds for the dimension of cohomology groups of frobeniusian Lie algebras. Moreover, it is shown that for a dense open subset of ${\mathbb{C}}^{p-1}$ the deformations of model algebras also belong to the family. Therefore any frobeniusian non-model algebra contracts on some element of the model whose parameters move on a finite union of hyperplanes. Further applications as the nullity of Rim's quadratic map $s{q}_1$ are obtained.

Cited by in corpus (1)

• Lie algebras : Classification, Deformations and Rigidity