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Full Description
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.
Contents
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.
