On the Brauer-Picard group of a finite symmetric tensor category

Academic Article


  • Let C_n denote the representation category of a finite supergroup generated by purely odd n-dimensional vector space. We compute the Brauer-Picard group BrPic(C_n) of C_n. This is done by identifying BrPic(C_n) with the group of braided tensor autoequivalences of the Drinfeld center of C_n and studying the action of the latter group on the categorical Lagrangian Grassmannian of C_n. We show that this action corresponds to the action of a projective symplectic group on a classical Lagrangian Grassmannian.
  • Authors

  • Bontea, Costel-Gabriel
  • Nikshych, Dmitri
  • Status

    Publication Date

  • October 15, 2015
  • Has Subject Area

    Published In

  • Journal of Algebra  Journal
  • Keywords

  • Brauer-Picard group
  • Drinfeld double
  • Hopf algebras
  • Tensor categories
  • Digital Object Identifier (doi)

    Start Page

  • 187
  • End Page

  • 218
  • Volume

  • 440