Non-splitting in Kirchberg's Ideal-related KK-Theory
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Non-splitting in Kirchberg's Ideal-related KK-Theory. / Eilers, Søren; Restorff, Gunnar; Ruiz, Efren.
I: Canadian Mathematical Bulletin, Bind 54, 2011, s. 68-81.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Non-splitting in Kirchberg's Ideal-related KK-Theory
AU - Eilers, Søren
AU - Restorff, Gunnar
AU - Ruiz, Efren
PY - 2011
Y1 - 2011
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
VL - 54
SP - 68
EP - 81
JO - Canadian Mathematical Bulletin
JF - Canadian Mathematical Bulletin
SN - 0008-4395
ER -
ID: 32472050