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arXiv · 0801.0324

Nonsplitting in Kirchberg's ideal-related KK-theory

Soren Eilers·Gunnar Restorff·Efren Ruiz
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Abstract

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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Soren Eilers, Gunnar Restorff, Efren Ruiz. 2008-01-02. Nonsplitting in Kirchberg's ideal-related KK-theory. https://doi.org/10.4153/cmb-2010-083-7

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