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

Abstract

AbstractWe 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.