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

Published online by Cambridge University Press:  20 November 2018

Evelyn Weimar-Woods
Evelyn Weimar-Woods*
Affiliation:
Fachbereich für Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, D-14195 Berlin, Germany e-mail: weimar@math.fu-berlin.de
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Abstract

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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

17B0517B70Lie algebrasgraded contractions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 6 , 01 December 2006 , pp. 1291 - 1340
Copyright
Copyright © Canadian Mathematical Society 2006

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