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Leibniz and Lie Algebra Structures for Nambu Algebra

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Abstract

We canonically associate a Leibniz algebra with every Nambu algebra. We show how various homological and cohomological complexes for a Nambu algebra can be naturally obtained from its structure as a module over the Leibniz algebra. We also present a generalization of a classical Lie--Berezin construction for Nambu algebras and extend these results for Nambu superalgebras.

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Authors and Affiliations

  1. National Technical University of Ukraine, 37 Peremogy prosp., Kiev, 252056, Ukraine

    Yuri L. Daletskii

  2. Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY, 11794-3651, U.S.A.

    Leon A. Takhtajan

Authors
  1. Yuri L. Daletskii
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  2. Leon A. Takhtajan
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Daletskii, Y.L., Takhtajan, L.A. Leibniz and Lie Algebra Structures for Nambu Algebra. Letters in Mathematical Physics 39, 127–141 (1997). https://doi.org/10.1023/A:1007316732705

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