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Nambu structures and associated bialgebroids

  • Samik Basu
  • Somnath Basu
  • Apurba Das
  • Goutam Mukherjee
Article
  • 74 Downloads

Abstract

We investigate higher-order generalizations of well known results for Lie algebroids 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.

Keywords

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

2010 Mathematics Subject Classification

Primary: 17B62 17B63 Secondary: 53C15 53D17 

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Stat-Math Unit, Indian Statistical InstituteKolkataIndia
  2. 2.Department of Mathematics and StatisticsIndian Institute of Science Education and ResearchMohanpurIndia

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