Non-solvable contractions of semisimple Lie algebras in low dimension

Details Non-solvable contractions of semisimple Lie algebras in low dimension Non-solvable contractions of semisimple Lie algebras in low dimension

2007-06-01

arxiv.org/abs/0706.0222v1

J.Phys.A40:5355-5372,2007

Physics

High Energy Physics

High Energy Physics - Theory

21 pages. 2 Tables, 2 figures

Scientific paper

10.1088/1751-8113/40/20/008

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.

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