arXiv subjects

Apurba Das

Publications and source records attributed to Apurba Das.

93 records · Page 6Linked to original sources

arXiv2017

Multiplicative Nambu structures on Lie groupoids

We study some properties of coisotropic submanifolds of a manifold with respect to a given multivector field. Using this notion, we generalize the results of Weinstein \cite{wein} 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 the infinitesimal version of Nambu-Lie groupoid is the notion of weak Lie-Filippov bialgebroid as introduced in \cite{bas-bas-das-muk}. Next we introduce coisotropic subgroupoids of a Nambu-Lie groupoid and these subgroupoids corresponds to, so called coisotropic subalgebroids of the corresponding weak Lie-Filippov bialgebroid.

math.DG↗

arXiv2015

On Generalized Lie Bialgebroids

An alternative proof of the duality of generalized Lie bialgebroid is given and proved a canonical Jacobi structure can be defined on the base of it. We also introduce the notion of morphism between generalized Lie bialgebroids and proved that the induced Jacobi structure is unique upto a morphism.

math-ph↗

arXiv2014

Modular Class of a Lie algebroid with a Nambu structure

In this paper, we introduce the notion of modular class of a Lie algebroid $A$ equipped with a Nambu structure satisfying some suitable hypothesis. We also introduce cohomology and homology theories for such Lie algebroids and prove that these theories are connected by a duality isomorphism when the modular class is null.

math.DG↗