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Journal of the Ramanujan Mathematical Society

Volume 35, Issue 3, September 2020  pp. 277–298.

Multiplicative Nambu structures on Lie groupoids

Authors:  Apurba Das
Author institution:Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208 016, Uttar Pradesh, India

Summary:  We study some properties of coisotropic submanifolds of a manifold with respect to a given multivector field. Using this notion, we generalize two main results of Weinstein [24] from Poisson bivector field to Nambu-Poisson tensor or more generally to any multivector field. We also introduce the notion of Nambu-Lie groupoid generalizing the concepts of both Poisson-Lie groupoid and Nambu-Lie group. We show that under certain cohomological restriction, Nambu-Lie groupoids give rise to weak Lie-Filippov bialgebroids as introduced in [1]. Next, we introduce coisotropic subgroupoids of a Nambu-Lie groupoid and these subgroupoids correspond to, so-called coisotropic subalgebroids of the corresponding weak Lie-Filippov bialgebroid.

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