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

Søren Eilers; Gunnar Restorff; Efren Ruiz

doi:10.4153/CMB-2010-083-7

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

Søren Eilers, Gunnar Restorff, Efren Ruiz

Department of Mathematical Sciences

4 Citations (Scopus)

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.

Original language	English
Journal	Canadian Mathematical Bulletin
Volume	54
Pages (from-to)	68-81
ISSN	0008-4395
DOIs	https://doi.org/10.4153/CMB-2010-083-7
Publication status	Published - Mar 2011

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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.",

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AU - Eilers, Søren

AU - Restorff, Gunnar

AU - Ruiz, Efren

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N2 - 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.

AB - 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.

U2 - 10.4153/CMB-2010-083-7

DO - 10.4153/CMB-2010-083-7

M3 - Journal article

SN - 0008-4395

VL - 54

SP - 68

EP - 81

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

ER -