09-147 R. Campoamor-Stursberg
Contractions of exceptional Lie algebras and semidirect products (304K, PDF) Aug 26, 09
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Abstract. For any semisimple subalgebra $\frak{s}^{\prime}$ of exceptional Lie algebras $\frak{s}$ satisfying the constraint ${\rm rank}(\frak{s}^{\prime})={\rm rank}(\frak{s})-1$ we analyze the branching rules for the adjoint representation, and determine the compatibility of the components with Heisenberg algebras. The analysis of these branching rules allows to classify the contractions of exceptional algebras onto semidirect products of semisimple and Heisenberg Lie algebras. Applications to the Schr\"odinger algebras are given.

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