Classification of Actions of Discrete Kac Algebras on Injective Factors

ISBN-13: 9781470420550 / Angielski

Toshihiko Masuda;Reiji Tomatsu

Opis

The authors study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. They 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, the authors show that the Connes-Takesaki module is a complete invariant.

Spis treści

• Introduction
• Preliminary
• Canonical extension of irreducible endomorphisms
• Kac algebras
• Classification of modular kernels
• Classification of actions with non-trivial modular parts
• Classification of centrally free actions
• Related problems
• Appendix
• Bibliography
• Index.