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Commutative algebras in Drinfeld categories of abelian Lie algebras

Part of: Categories with structure Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  30 August 2012

Alexei Davydov  and
Vyacheslav Futorny
Alexei Davydov
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Vyacheslav Futorny
Affiliation:
Institute of Mathematics and Statistics, University of São Paulo, CEP 05315-970, São Paulo, Brazil ([email protected])
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Abstract

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We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over these algebras and classify commutative algebras with a finite number of simple local modules.

Keywords

monoidal categoryDrinfeld categorymetric Lie algebralocal module

MSC classification

Secondary: 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories 17B10: Representations, algebraic theory (weights)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 3 , October 2012 , pp. 613 - 633
Copyright
Copyright © Edinburgh Mathematical Society 2012

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