Nambu structures on Lie algebroids and their modular classes

Article Type

Research Article

Publication Title

Proceedings of the Indian Academy of Sciences: Mathematical Sciences


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.



Publication Date



Open Access, Green