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

Open Access article
 Printed: Dec 2006
  • Evelyn Weimar-Woods
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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.
Keywords: Lie algebras, graded contractions Lie algebras, graded contractions
MSC Classifications: 17B05, 17B70 show english descriptions Structure theory
Graded Lie (super)algebras
17B05 - Structure theory
17B70 - Graded Lie (super)algebras

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