arXiv subjects
Publications and source records attributed to R. Campoamor.
We determine the solvable complete Lie algebras whose nilradical is isomorphic to a filiform Lie algebra. Moreover we show that for any positive integer $n$ there exists a solvable complete Lie algebras whose second cohomology group with values in the adjoint module has dimension at least $n$.
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.