Classification of actions of discrete Kac algebras on injective factors

Abstract

We will study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. We will construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, we will show that the Connes-Takesaki module is a complete invariant.

120 pages. Minor corrections

References in corpus (3)

• Co-Amenability of compact quantum groups
• Classification of minimal actions of a compact Kac algebra with amenable dual
• Rohlin flows on von Neumann algebras

Cited by in corpus (2)

• Asymptotic structure of free product von Neumann algebras
• Connes' bicentralizer problem for q-deformed Araki-Woods algebras