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The Orbit Method in Geometry and Physics pp 101–146Cite as

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Defining Relations for the Exceptional Lie Superalgebras of Vector Fields

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Part of the book series: Progress in Mathematics ((PM,volume 213))

Abstract

We list defining relations for four of the five exceptional simple Lie superalgebras of vector fields with polynomial coefficients. This is done for one of many inequivalent systems of simple roots (generators). For the fifth superalgebra the result is not final: there might be infinitely many relations. On the contrary, for the same Lie super-algebra with Laurent polynomials as coefficients there are only finitely many relations. To show perspective, the complete list of simple complex vectorial Lie superalgebras is given, and their relations have been calculated (also for one system of generators only) in [GLP].

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Stockholm, Roslagsv. 101 Kräftriket hus 6, SE-10691, Stockholm, Sweden

    Pavel Grozman & Dimitry Leites

  2. Independent University of Moscow, Bolshoj Vlasievsky per, RU-121002, Moscow, Russia

    Irina Shchepochkina

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  1. Pavel Grozman
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  2. Dimitry Leites
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  3. Irina Shchepochkina
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Editors and Affiliations

  1. Centre de Physique Théorique CNRS, Campus de Luminy, Marseille Cedex 9, F-13288, France

    Christian Duval

  2. Institut Girard Desargues, Université Claude Bernard Lyon 1, Villeurbanne Cedex, F-69622, France

    Valentin Ovsienko

  3. Département des Sciences Mathématiques, Université Montpellier II, Montpelier Cedex 5, F-34095, France

    Laurent Guieu

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Grozman, P., Leites, D., Shchepochkina, I. (2003). Defining Relations for the Exceptional Lie Superalgebras of Vector Fields. In: Duval, C., Ovsienko, V., Guieu, L. (eds) The Orbit Method in Geometry and Physics. Progress in Mathematics, vol 213. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0029-1_7

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  • DOI: https://doi.org/10.1007/978-1-4612-0029-1_7

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