On the cohomology of frobeniusian model Lie algebras

Details On the cohomology of frobeniusian model Lie algebras On the cohomology of frobeniusian model Lie algebras

2001-12-21

arxiv.org/abs/math/0112241v1

Mathematics

Rings and Algebras

Scientific paper

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 $sq_{1}$ are obtained.

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