- 09-147 R. Campoamor-Stursberg
- Contractions of exceptional Lie algebras and semidirect products
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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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