CLASSIFICATION OF APPROXIMATELY INNER ACTIONS OF DISCRETE AMENABLE GROUPS ON STRONGLY AMENABLE SUBFACTORS

We give the classification theorem of approximately inner actions of discrete amenable groups on strongly amenable subfactor of type II1by means of the characteristic invariant and ν invariant. To prove this theorem, we also give the classification theorem when the inner part and the centrally trivial part of actions coincide.

Characteristic invatiant of tensor product actions and actions on crossed products

The first purpose of this paper is to give a tensor product formula of the characteristic invariant and modular invariant for a tensor product action of a discrete group G on AFD factors. The second purpose is to describe a characteristic invariant and modular invariant of the extended action to a crossed product in terms of the original invariants.