Nambu structures on Lie algebroids and their modular classes

Authors

Apurba Das, Indian Statistical Institute, Kolkata
Shilpa Gondhali, Birla Institute of Technology and Science, Pilani
Goutam Mukherjee, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Abstract

We introduce the notion of the modular class of a Lie algebroid equipped with a Nambu structure. In particular, we recover the modular class of a Nambu–Poisson manifold M with its Nambu tensor Λ as the modular class of the tangent Lie algebroid TM with Nambu structure Λ. We show that many known properties of the modular class of a Nambu–Poisson manifold and that of a Lie algebroid extend to the setting of a Lie algebroid with Nambu structure. Finally, we prove that for a large class of Nambu–Poisson manifolds considered as tangent Lie algebroids with Nambu structures, the associated modular classes are closely related to Evens–Lu–Weinstein modular classes of Lie algebroids.

DOI

10.1007/s12044-019-0496-6

Publication Date

9-1-2019

Comments

Open Access, Green

Recommended Citation

Das, Apurba; Gondhali, Shilpa; and Mukherjee, Goutam, "Nambu structures on Lie algebroids and their modular classes" (2019). Journal Articles. 726.
https://digitalcommons.isical.ac.in/journal-articles/726