Non-solvable contractions of semisimple Lie algebras in low dimension

Abstract

The problem of non-solvable contractions of Lie algebras is analyzed. By means of a stability theorem, the problem is shown to be deeply related to the embeddings among semisimple Lie algebras and the resulting branching rules for representations. With this procedure, we determine all deformations of indecomposable Lie algebras having a nontrivial Levi decomposition onto semisimple Lie algebras of dimension $n\leq 8$, and obtain the non-solvable contractions of the latter class of algebras.