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Universal Enveloping Algebras of Lie Antialgebras |
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| Authors: | Séverine Leidwanger Sophie Morier-Genoud |
| Institution: | 1. Institut Math??matiques de Jussieu, Th??orie des groupes, Universit?? Denis Diderot Paris 7, Case 7012, 75205, Paris Cedex 13, France 2. Institut Math??matiques de Jussieu, Universit?? Pierre et Marie Curie Paris 6, 4 place Jussieu, case 247, 75252, Paris Cedex 05, France |
| 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. |
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