The structure of the automorphism group of an injective factor and the cocycle conjugacy of discrete abelian group actions

Abstract

We complete classification of discrete abelian or finite group actions on injective type III1 factors up to cocycle conjugacy. We also give a proof for Connes’ characterization of the Ker (mod) and Cnt(M) for an injective factor M of type III. §0 Introduction. The purpose of this paper is to give a proof of Connes’ announcement on approximately inner automorphisms and centrally trivial automorphisms of an injective 1980 Mathematics Subject Classification (1985 Revision). 46L40.