A characterization of depth 2 subfactors of II1 factors

Academic Article


  • We characterize finite index depth 2 inclusions of type II_1 factors in terms of actions of weak Kac algebras and weak C*-Hopf algebras. If N\subset M \subset M_1 \subset M_2 \subset ... is the Jones tower constructed from such an inclusion N\subset M, then B=M^\prime \cap M_2 has a natural structure of a weak C*-Hopf algebra and there is a minimal action of B on M_1 such that M is the fixed point subalgebra of M_1, and M_2 is isomorphic to the crossed product of M_1 and B. This extends the well-known results for irreducible depth 2 inclusions.
  • Authors

  • Nikshych, Dmitri
  • Vainerman, L
  • Status

    Publication Date

  • March 10, 2000
  • Has Subject Area

    Published In


  • math.OA
  • math.QA
  • Digital Object Identifier (doi)

    Start Page

  • 278
  • End Page

  • 307
  • Volume

  • 171
  • Issue

  • 2