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arXiv · 1610.01184

Nambu structures on Lie algebroids and their modular classes

Apurba Das·Shilpa Gondhali·Goutam Mukherjee
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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 that of a Lie algebropid 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.

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Apurba Das, Shilpa Gondhali, Goutam Mukherjee. 2016-09-16. Nambu structures on Lie algebroids and their modular classes. https://arxiv.org/abs/1610.01184

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