CLASSIFICATION OF ACTIONS OF DISCRETE AMENABLE GROUPS ON AMENABLE SUBFACTORS OF TYPE II
نویسندگان
چکیده
منابع مشابه
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...
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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...
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Using the continuous decomposition, we classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type IIIλ, 0 < λ < 1. Winsløw’s fundamental homomorphism is a complete invariant. This removes the extra assumptions in the classification theorems of Loi and Winsløw and gives a complete classification up to cocycle conjugacy.
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It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Čech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete groups. In [KW], Kirchberg and Wassermann discussed exactness for groups. A discrete group G is said to be exact if its reduced group C-algebra C λ(G) is exact. Th...
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ژورنال
عنوان ژورنال: International Journal of Mathematics
سال: 2010
ISSN: 0129-167X,1793-6519
DOI: 10.1142/s0129167x10006343