Classification of Minimal Actions of a Compact Kac Algebra with Amenable Dual on Injective Factors of Type Iii
نویسنده
چکیده
We classify a certain class of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III. Our main technical tools are the structural analysis of type III factors and the theory of canonical extension of endomorphisms introduced by Izumi.
منابع مشابه
Classification of Minimal Actions of a Compact Kac Algebra with the Amenable Dual
We show the uniqueness of minimal actions of a compact Kac algebra with the amenable dual on the AFD factor of type II1. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.
متن کاملCharacterizations of amenable hypergroups
Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.
متن کاملAmenability and co-amenability in non-abelian group duality
Leptin’s theorem asserts that a locally compact group is amenable if and only if its Fourier algebra has a bounded (by one) approximate identity. In the language of locally compact quantum groups—in the sense of J. Kustermans and S. Vaes—, it states that a locally compact group is amenable if and only if its quantum group dual is co-amenable. It is an open problem whether this is true for gener...
متن کامل2 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.
متن کاملAmenability and Weak Amenability of the Semigroup Algebra l^1 (〖 S〗_T )
Let S be a semigroup with a left multiplier on S. A new product on S is defined by related to S and such that S and the new semigroup ST have the same underlying set as S. It is shown that if is injective then where, is the extension of on Also, we show that if is bijective then is amenable if and only if is so. Moreover, if S completely regular, then is weakly amenable.
متن کامل