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On the cohomology of frobeniusian model Lie algebras

J. M. Ancochea·R. Campoamor
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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 $sq_{1}$ are obtained.

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J. M. Ancochea, R. Campoamor. 2001-12-21. On the cohomology of frobeniusian model Lie algebras. https://arxiv.org/abs/math/0112241

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