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Symmetries Wider than Supersymmetry

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Book cover Noncommutative Structures in Mathematics and Physics

Part of the book series: NATO Science Series ((NAII,volume 22))

Abstract

We observe that supersymmetries do not exhaust all the symmetries of the supermanifolds. On a generalization of supermanifolds (called metamanifolds), the “functions” form a metaabelean algebra, i.e., the one for which [[ x, y],z] = 0 with respect to the usual commutator. The superspaces considered as metaspaces admit symmetries wider than supersymmetries. Conjecturally, infinitesimal transformations of these metaspaces constitute Volichenko algebras which we introduce as inhomogeneous subalgebras of Lie superalgebras. The Volichenko algebras are natural generalizations of Lie superalgebras being 2-step filtered algebras. They are non-conventional deformations of Lie algebras bridging them with Lie superalgebras.

Instead of 1. Naudts contribution by the editor S. Duplij’s request

D.L. is thankful to an NFR grant for partial financial support, to V. Molotkov, A. Premet and S. Majid for help.

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Authors and Affiliations

  1. Department of Mathematics, University of Stockholm, Roslagsvägen. 101, Kräftriket hus 6, S-106 91, Stockholm, Sweden

    Dimitry Leites

  2. Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA

    Vera Serganova

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  1. Dimitry Leites
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  2. Vera Serganova
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Editors and Affiliations

  1. Theory Group, Nuclear Physics Laboratory, Kharkov National University, Kharkov, Ukraine

    Steven Duplij

  2. Sektion Physik, Ludwig-Maximillians-Universität, München, Germany

    Julius Wess

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Leites, D., Serganova, V. (2001). Symmetries Wider than Supersymmetry. In: Duplij, S., Wess, J. (eds) Noncommutative Structures in Mathematics and Physics. NATO Science Series, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0836-5_2

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  • DOI: https://doi.org/10.1007/978-94-010-0836-5_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6999-8

  • Online ISBN: 978-94-010-0836-5

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