Nambu structures and associated bialgebroids

Authors

Samik Basu, Indian Statistical Institute, Kolkata
Somnath Basu, Indian Institute of Science Education and Research Kolkata
Apurba Das, Indian Statistical Institute, Kolkata
Goutam Mukherjee, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

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.

DOI

10.1007/s12044-018-0455-7

Publication Date

2-1-2019

Comments

Open Access, Green

Recommended Citation

Basu, Samik; Basu, Somnath; Das, Apurba; and Mukherjee, Goutam, "Nambu structures and associated bialgebroids" (2019). Journal Articles. 963.
https://digitalcommons.isical.ac.in/journal-articles/963