Frobenius extensions and weak Hopf algebras

Academic Article


  • We study a symmetric Markov extension of k-algebras N \into M, a certain kind of Frobenius extension with conditional expectation that is tracial on the centralizer and dual bases with a separability property. We place a depth two condition on this extension, which is essentially the requirement that the Jones tower N \into M \into M_1 \into M_2 can be obtained by taking relative tensor products with centralizers A = C_{M_1}(N) and B = C_{M_2}(M). Under this condition, we prove that N \into M is the invariant subalgebra pair of a weak Hopf algebra action by A, i.e., that N = M^A. The endomorphism algebra M_1 = \End_N M is shown to be isomorphic to the smash product algebra M # A. We also extend results of Szymanski, Vainerman and the second author, and the authors.
  • Authors

  • Kadison, L
  • Nikshych, Dmitri
  • Status

    Publication Date

  • October 1, 2001
  • Has Subject Area

    Published In

  • Journal of Algebra  Journal
  • Keywords

  • Frobenius extension
  • Jones tower
  • actions
  • basic construction
  • conditional expectation
  • endomorphism ring
  • symmetric Markov extension
  • trace
  • weak Hopf algebra
  • Digital Object Identifier (doi)

    Start Page

  • 312
  • End Page

  • 342
  • Volume

  • 244
  • Issue

  • 1