Article

Algebras and Representation Theory

, Volume 15, Issue 1, pp 1-27

Universal Enveloping Algebras of Lie Antialgebras

  • Séverine LeidwangerAffiliated withInstitut Mathématiques de Jussieu, Théorie des groupes, Université Denis Diderot Paris 7
  • , Sophie Morier-GenoudAffiliated withInstitut Mathématiques de Jussieu, Université Pierre et Marie Curie Paris 6 Email author 

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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

Jordan superalgebra Lie superalgebra Universal enveloping algebra

Mathematics Subject Classifications (2010)

17C50 17C70 17B60