C*-代数上直至等变kk等价的群作用的分类

R. Meyer
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引用次数: 13

摘要

研究了C*-代数上群作用的分类,直到等变kk等价。我们证明了任何群作用都等价于一个简单的纯无限C*-代数上的一个作用。证明了与Izumi的一个猜想等价于Kirchberg代数上无扭转可调群作用的环共轭和等变kk等价。设G是一个素阶的循环群。根据Manuel Kohler之前的工作,我们描述了它的作用直到等变kk等价。特别地,我们将G在稳定的Cuntz代数上的作用分类为等变自举类直到等变kk等价。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the classification of group actions on C*-algebras up to equivariant KK-equivalence
We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. We show that any group action is equivariantly KK-equivalent to an action on a simple, purely infinite C*-algebra. We show that a conjecture of Izumi is equivalent to an equivalence between cocycle conjugacy and equivariant KK-equivalence for actions of torsion-free amenable groups on Kirchberg algebras. Let G be a cyclic group of prime order. We describe its actions up to equivariant KK-equivalence, based on previous work by Manuel Kohler. In particular, we classify actions of G on stabilised Cuntz algebras in the equivariant bootstrap class up to equivariant KK-equivalence.
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