• Nambu structures on Lie algebroids and their modular classes

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/129/04/0059

• # Keywords

Lie algebroid; Nambu–Poisson manifold; Leibniz algebra cohomology; Leibniz algebroid; modular class

• # 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 $\Lambda$ as the modular class of the tangent Lie algebroid $TM$ with Nambu structure $\Lambda$. 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.

• # Author Affiliations

1. Stat.-Math. Unit, Indian Statistical Institute, Kolkata 700 108, India
2. Department of Mathematics, Birla Institute of Technology and Sciences, Pilani, K. K. Birla Goa Campus, Goa 403 726, India

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019