Abstract view
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Non-splitting in Kirchberg's Ideal-related $KK$-Theory
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Published:2010-08-03
Printed: Mar 2011
Søren Eilers,
Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark
Gunnar Restorff,
Faculty of Science and Technology, University of Faroe Islands, Tórshavn, Faroe Islands
Efren Ruiz,
Department of Mathematics, University of Hawaii Hilo, Hilo, Hawaii, U.S.A
Abstract
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.
