Nonsplitting in Kirchberg's ideal-related KK-theory

Details Nonsplitting in Kirchberg's ideal-related KK-theory Nonsplitting in Kirchberg's ideal-related KK-theory

2008-01-02

arxiv.org/abs/0801.0324v3

Mathematics

Operator Algebras

14 pages, minor typos fixed, 5 figures added

Scientific paper

A universal coefficient theorem in the setting of Kirchberg's ideal-related KK-theory was obtained in the fundamental case of a C*-algebra with one specified ideal by Bonkat and proved there to split, unnaturally, under certain conditions. Employing certain K-theoretical information derivable from the given operator algebras in a way 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.

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