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# The General Structure of $G$-Graded Contractions of Lie Algebras I. The Classification

Published:2006-12-01
Printed: Dec 2006
• Evelyn Weimar-Woods
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## Abstract

We give the general structure of complex (resp., real) $G$-graded contractions of Lie algebras where $G$ is an arbitrary finite Abelian group. For this purpose, we introduce a number of concepts, such as pseudobasis, higher-order identities, and sign invariants. We characterize the equivalence classes of $G$-graded contractions by showing that our set of invariants (support, higher-order identities, and sign invariants) is complete, which yields a classification.