M ar 1 99 7 Classification of actions of discrete amenable groups on strongly amenable subfactors of type III

Classification of Strongly Free Actions of Discrete Amenable Groups on Strongly Amenable Subfactors of Type Iii0

In the theory of operator algebras, classification of group actions on approximately finite dimensional (AFD) factors has been done since Connes’s work [2]. In subfactor theory, various results on classification of group actions have been obtained. The most powerful results have been obtained by Popa in [16], who classified the strongly outer actions of discrete amenable groups on strongly amen...

Classification of Actions of Discrete Amenable Groups on Amenable Subfactors of Type Ii

We prove a classification result for properly outer actions σ of discrete amenable groups G on strongly amenable subfactors of type II, N ⊂ M , a class of subfactors that were shown to be completely classified by their standard invariant GN,M , in ([Po7]). The result shows that the action σ is completely classified in terms of the action it induces on GN,M . As a an application of this, we obta...

2 N ov 2 01 6 Classification of Roberts actions of strongly amenable C ∗ - tensor categories on the injective factor of type III 1 Toshihiko MASUDA

In this paper, we generalize Izumi’s result on uniqueness of realization of finite C-tensor categories in the endomorphism category of the injective factor of type III1 for finitely generated strongly amenable C -tensor categories by applying Popa’s classification theorem of strongly amenable subfactors of type III1.

Structural Properties of Inner Amenable Discrete Groups

A CHARACTERIZATION OF EXTREMELY AMENABLE SEMIGROUPS

Let S be a discrete semigroup, m (S) the space of all bounded real functions on S with the usualsupremum norm. Let Acm (S) be a uniformly closed left invariant subalgebra of m (S) with 1 c A. We say that A is extremely left amenable if there isamultiplicative left invariant meanon A. Let P = {h ?A: h =|g-1,g | forsome g ?A, s ?S}. It isshown that . A is extremely left amenable if and only ...