1. CJM 2006 (vol 58 pp. 1291)
|The General Structure of $G$-Graded Contractions of Lie Algebras I. The Classification |
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