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    • Fulltext

       

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      Permanent link:
      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

       

      APURBA DAS1 SHILPA GONDHALI2 GOUTAM MUKHERJEE1

      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

    • Dates

       
      Published
      1 September 2019
      Manuscript received
      3 August 2018
      Manuscript revised
      Accepted
      29 August 2018
      Early published
      Unedited version published online
      Final version published online
      24 June 2019

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