{"title":"On the classification of group actions on C*-algebras up to equivariant KK-equivalence","authors":"R. Meyer","doi":"10.2140/akt.2021.6.157","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":"2018 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/akt.2021.6.157","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
Abstract
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.