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