2011-01-01, English, Article, Journal or magazine article edition: Lie antialgebras: Premices. Ovsienko, V.

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Physical Description
  • Magazine/​Journal article
Published
  • Elsevier B.V., 2011 Jan 1
Language
  • English

Edition details

Title
  • Lie antialgebras: Premices.
Appears In
  • Journal of Algebra, v.325, no.1, 2011 Jan 1, p.216(32) (ISSN: 0021-8693)
Author
  • Ovsienko, V.
Published
  • Elsevier B.V., 2011 Jan 1
Physical Description
  • Magazine/​Journal article
Subjects
Target Audience
  • Academic
Summary
  • To link to full-text access for this article, visit this link: http:/​/​dx.doi.org/​10.1016/​j.jalgebra.2010.10.003 Byline: V. Ovsienko Keywords: Graded commutative algebras; Lie superalgebras; Symplectic geometry Abstract: The main purpose of this work is to develop the basic notions of the Lie theory for commutative algebras. We introduce a class of Z.sub.2-graded commutative but not associative algebras that we call "Lie antialgebras". These algebras form a very special class of Jordan superalgebras, they are closely related to Lie (super)algebras and, in some sense, link together commutative and Lie algebras. The main notions we define in this paper are: representations of Lie antialgebras, an analog of the Lie-Poisson bivector (which is not Poisson) and central extensions. We will explain the geometric origins of Lie antialgebras and provide a number of examples. We also classify simple finite-dimensional Lie antialgebras. This paper is a new version of the unpublished preprint Ovsienko . Author Affiliation: CNRS, Institut Camille Jordan, Universite Lyon 1, Villeurbanne Cedex, F-69622, France Article History: Received 7 February 2010 Article Note: (miscellaneous) Communicated by Efim Zelmanov
Terms of Use
  • COPYRIGHT 2011 Elsevier B.V.
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 242603437

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