Hopf algebra actions on strongly separable extensions of depth two

Academic Article


  • We bring together ideas in analysis of Hopf *-algebra actions on II_1 subfactors of finite Jones index and algebraic characterizations of Frobenius, Galois and cleft Hopf extensions to prove a non-commutative algebraic analogue of the classical theorem: a finite field extension is Galois iff it is separable and normal. Suppose N < M is a separable Frobenius extension of k-algebras split as N-bimodules with a trivial centralizer C_M(N). Let M_1 := End(M)_N and M_2 := End(M_1)_M be the endomorphism algebras in the Jones tower N < M < M_1 < M_2. We show that under depth 2 conditions on the second centralizers A := C_{M_1}(N) and B : = C_{M_2}(M) the algebras A and B are semisimple Hopf algebras dual to one another and such that M_1 is a smash product of M and A, and that M is a B-Galois extension of N.
  • Authors

  • Kadison, L
  • Nikshych, Dmitri
  • Status

    Publication Date

  • November 10, 2001
  • Has Subject Area

    Published In


  • 12F10,16W30, 22D30, 46L37
  • math.QA
  • math.RA
  • Digital Object Identifier (doi)

    Start Page

  • 258
  • End Page

  • 286
  • Volume

  • 163
  • Issue

  • 2