Duality for actions of weak Kac algebras and crossed product inclusions of II1 factors

Academic Article


  • We show that indecomposable weak Kac algebras are free over their Cartan subalgebras and prove a duality theorem for their actions. Using this result, for any biconnected weak Kac algebra we construct a minimal action on the hyperfinite II_1 factor. The corresponding crossed product inclusion of II_1 factors has depth 2 and an integer index. Its first relative commutant is, in general, non-trivial, so we derive some arithmetic properties of weak Kac algebras from considering reduced subfactors.
  • Status

    Publication Date

  • 2001
  • Has Subject Area

    Published In


  • duality for actions
  • lambda-lattices
  • subfactors
  • weak Kac algebras
  • Start Page

  • 635
  • End Page

  • 655
  • Volume

  • 46
  • Issue

  • 3