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Generalized Reduced Enveloping Algebras for Restricted Lie Algebras

✍ Scribed by Christopher P Bendel

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 272 KB
Volume: 218
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7876

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✦ Synopsis

We observe that any finite-dimensional indecomposable module for a restricted Lie algebra over an algebraically closed field is a module for a finite-dimensional quotient of the universal enveloping algebra. These algebras form a two-parameter family which generalizes the notion of a reduced enveloping algebra. We identify each such algebra as a reduced enveloping algebra for an associated Lie algebra and use this to compute support varieties and obtain some representation-theoretic consequences.

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