Non-splitting in Kirchberg's Ideal-related $KK$-Theory

Canadian mathematical bulletin

Efren Ruiz²  Søren Eilers³  Gunnar Restorff¹ 

[1] Faculty of Science and Technology, University of Faroe Islands, Tórshavn, Faroe Islands;Department of Mathematics, University of Hawaii Hilo, Hilo, Hawaii, U.S.A;Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

关键词: KK-theory;    UCT;   

DOI  :  10.4153/CMB-2010-083-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

A. Bonkat obtained a universal coefficient theorem in the setting of Kirchberg'sideal-related $KK$-theory in the fundamental case of a$C^*$-algebra with onespecified ideal. The universal coefficient sequence was shown to split, unnaturally, under certainconditions. Employing certain $K$-theoretical information derivablefrom the given operator algebras using a method introduced here, we shalldemonstrate that Bonkat's UCT does not split in general. Relatedmethods lead to information on the complexity of the $K$-theory whichmust be used toclassify $*$-isomorphisms for purely infinite $C^*$-algebras withone non-trivial ideal.

【 授权许可】

Unknown