Algebras and Representation Theory

, Volume 15, Issue 1, pp 1–27

Universal Enveloping Algebras of Lie Antialgebras


  • Séverine Leidwanger
    • Institut Mathématiques de Jussieu, Théorie des groupesUniversité Denis Diderot Paris 7
    • Institut Mathématiques de JussieuUniversité Pierre et Marie Curie Paris 6

DOI: 10.1007/s10468-010-9230-x

Cite this article as:
Leidwanger, S. & Morier-Genoud, S. Algebr Represent Theor (2012) 15: 1. doi:10.1007/s10468-010-9230-x


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.


Jordan superalgebraLie superalgebraUniversal enveloping algebra

Mathematics Subject Classifications (2010)


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© Springer Science+Business Media B.V. 2010