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

http://dx.doi.org/10.4153/CJM-2006-046-x
Canad. J. Math. 58(2006), 1291-1340

  Published:2006-12-01
 Printed: Dec 2006

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.