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    • 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



      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

  • Proceedings – Mathematical Sciences | News

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