Universal Enveloping Algebras of Lie Antialgebras
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.
KeywordsJordan superalgebra Lie superalgebra Universal enveloping algebra
Mathematics Subject Classifications (2010)17C50 17C70 17B60
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