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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/129/01/0012

    • Keywords

       

      $n$-Ary operation; Nambu–Poisson bracket; Gerstenhaber bracket; Lie bialgebroid

    • Abstract

       

      We investigate higher-order generalizations of well known results for Liealgebroids and bialgebroids. It is proved that $n$-Lie algebroid structures correspond to $n$-ary generalization of Gerstenhaber algebras and are implied by $n$-ary generalization of linear Poisson structures on the dual bundle. A Nambu–Poisson manifold (of order $n$ > 2) gives rise to a special bialgebroid structure which is referred to as a weak Lie–Filippov bialgebroid (of order $n$). It is further demonstrated that such bialgebroids canonically induce a Nambu–Poisson structure on the base manifold. Finally, the tangent space of a Nambu Lie group gives an example of a weak Lie–Filippov bialgebroid over a point.

    • Author Affiliations

       

      SAMIK BASU1 SOMNATH BASU2 APURBA DAS1 GOUTAM MUKHERJEE1

      1. Stat-Math Unit, Indian Statistical Institute, Kolkata 700 108, India
      2. Department of Mathematics and Statistics, Indian Institute of Science Education and Research, Mohanpur 741 246, India

    • Dates

       
      Published
      1 February 2019
      Manuscript received
      13 July 2017
      Manuscript revised
      18 December 2017
      Accepted
      22 December 2017
      Early published
      Unedited version published online
      Final version published online
      18 December 2018

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