Geodesic
Non-splitting in Kirchberg's Ideal-related KK-Theory
Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 68-81

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DOI

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 $\text{UCT}$ 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.
DOI : 10.4153/CMB-2010-083-7
Mots-clés : 46L35, KK-theory, UCT 
Eilers, Søren; Restorff, Gunnar; Ruiz, Efren. Non-splitting in Kirchberg's Ideal-related KK-Theory. Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 68-81. doi: 10.4153/CMB-2010-083-7
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     title = {Non-splitting in {Kirchberg's} {Ideal-related} {KK-Theory}},
     journal = {Canadian mathematical bulletin},
     pages = {68--81},
     year = {2011},
     volume = {54},
     number = {1},
     doi = {10.4153/CMB-2010-083-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-083-7/}
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