Algebras and Representation Theory

, Volume 15, Issue 1, pp 1–27

Universal Enveloping Algebras of Lie Antialgebras

Article

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

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 superalgebraLie superalgebraUniversal enveloping algebra

Mathematics Subject Classifications (2010)

17C5017C7017B60

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Institut Mathématiques de Jussieu, Théorie des groupesUniversité Denis Diderot Paris 7Paris Cedex 13France
  2. 2.Institut Mathématiques de JussieuUniversité Pierre et Marie Curie Paris 6Paris Cedex 05France