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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/132/0002

    • Keywords

       

      Filippov algebroid; Filippov algebra; deformation; differential graded Lie algebra; deformation cohomology.

    • Abstract

       

      In this article, we study the deformations of Filippov algebroids. First, we define a differential graded Lie algebra for a Filippov algebroid by introducing the notion of Filippov multiderivations for a vector bundle. We then discuss deformations of a Filippov algebroid in terms of low-dimensional cohomology associated with this differential graded Lie algebra. We define Nijenhuis operators on Filippov algebroids and characterize trivial deformations of Filippov algebroids in terms of these operators. Finally, we define finite order deformations and discuss the problem of extending a given finite order deformation to a deformation of a higher order.

    • Author Affiliations

       

      SATYENDRA KUMAR MISHRA1 GOUTAM MUKHERJEE2 ANITA NAOLEKAR1

      1. Statistics and Mathematics Unit, Theoretical Statistics and Mathematics Division, Indian Statistical Institute, 8th Mile, Mysore Road, RVCE Post, Bangalore 560 059, India
      2. Statistics and Mathematics Unit, Theoretical Statistics and Mathematics Division, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700 108, India

    • Dates

       
      Published
      4 December 2021
      Manuscript received
      17 June 2020
      Manuscript revised
      27 January 2021
      Accepted
      21 January 2021
      Final version published online
      4 December 2021

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