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Universal Enveloping Algebras of Lie Antialgebras

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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.

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Authors and Affiliations

  1. Institut Mathématiques de Jussieu, Théorie des groupes, Université Denis Diderot Paris 7, Case 7012, 75205, Paris Cedex 13, France

    Séverine Leidwanger

  2. Institut Mathématiques de Jussieu, Université Pierre et Marie Curie Paris 6, 4 place Jussieu, case 247, 75252, Paris Cedex 05, France

    Sophie Morier-Genoud

Authors
  1. Séverine Leidwanger
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  2. Sophie Morier-Genoud
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Correspondence to Sophie Morier-Genoud.

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Leidwanger, S., Morier-Genoud, S. Universal Enveloping Algebras of Lie Antialgebras. Algebr Represent Theor 15, 1–27 (2012). https://doi.org/10.1007/s10468-010-9230-x

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  • DOI: https://doi.org/10.1007/s10468-010-9230-x

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