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

被引：4

作者：

Eilers, Soren ^{[1
]}

Restorff, Gunnar

Ruiz, Efren ^{[2
]}

机构：

[1] Univ Copenhagen, Dept Math Sci, Copenhagen, Denmark

[2] Univ Hawaii, Dept Math, Hilo, HI 96720 USA

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2011年 / 54卷 / 01期

关键词：

KK-theory; UCT; C-ASTERISK-ALGEBRAS; ONE NONTRIVIAL IDEAL; KASPAROV GROUPS; RORDAMS CLASSIFICATION; FUNCTOR; UCT;

D O I：

10.4153/CMB-2010-083-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A. Bonkat obtained a universal coefficient theorem in the setting of Kirchberg's ideal-related KK-theory in the fundamental case of a C*-algebra with one specified ideal. The universal coefficient sequence was shown to split, unnaturally, under certain conditions. Employing certain K-theoretical information derivable from the given operator algebras using a method introduced here, we shall demonstrate that Bonkat's UCT does not split in general. Related methods lead to information on the complexity of the K-theory which must be used to classify *-isomorphisms for purely infinite C*-algebras with one non-trivial ideal.

引用

页码：68 / 81

页数：14

共 19 条

[1]

BONKAT A, 2002, THESIS WESTFALISCHE

[2] A CLASS OF C-STAR-ALGEBRAS AND TOPOLOGICAL MARKOV-CHAINS .2. REDUCIBLE CHAINS AND THE EXT-FUNCTOR FOR C-STAR-ALGEBRAS [J].