Universal Enveloping Algebras of Lie Antialgebras
Commutative Algebra
2010-07-26 v2 Rings and Algebras
Representation Theory
Abstract
Lie antialgebras is a class of supercommutative algebras recently appeared in symplectic geometry. We define the notion of enveloping algebra of a Lie antialgebra and study its properties. We show that every Lie antialgebra is canonically related to a Lie superalgebra and prove that its enveloping algebra is a quotient of the enveloping algebra of the corresponding Lie superalgebra.
Keywords
Cite
@article{arxiv.0910.2220,
title = {Universal Enveloping Algebras of Lie Antialgebras},
author = {Séverine Leidwanger and Sophie Morier-Genoud},
journal= {arXiv preprint arXiv:0910.2220},
year = {2010}
}