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The problem of non-solvable contractions of Lie algebras is analyzed. Bymeans of a stability theorem, the problem is shown to be deeply related to theembeddings among semisimple Lie algebras and the resulting branching rules forrepresentations. With this procedure, we determine all deformations ofindecomposable Lie algebras having a nontrivial Levi decomposition ontosemisimple Lie algebras of dimension $n\leq 8$, and obtain the non-solvablecontractions of the latter class of algebras.

Non-solvable contractions of semisimple Lie algebras in low dimension