# 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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