Classification of minimal actions of a compact Kac algebra with amenable dual

Abstract

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II${}_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.

68 pages, Introduction rewritten; minor corrections

Cited by in corpus (5)

• Rohlin flows on von Neumann algebras
• Classification of actions of discrete Kac algebras on injective factors
• Berezin Quantization From Ergodic Actions of Compact Quantum Groups, and Quantum Gromov-Hausdorff Distance
• Approximate innerness and central triviality of endomorphisms
• Approximate Unitary Equivalence of Finite Index Endomorphisms of the AFD Factors