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1. CMB 2010 (vol 54 pp. 68)

Eilers, Søren; Restorff, Gunnar; Ruiz, Efren
Non-splitting in Kirchberg's Ideal-related $KK$-Theory
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.

Keywords:KK-theory, UCT
Category:46L35

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