Universal Enveloping Algebras of Lie Antialgebras
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- Leidwanger, S. & Morier-Genoud, S. Algebr Represent Theor (2012) 15: 1. doi:10.1007/s10468-010-9230-x
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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.