Nonsplitting in Kirchberg's ideal-related KK-theory
Operator Algebras
2013-09-05 v3
Abstract
A universal coefficient theorem in the setting of Kirchberg's ideal-related KK-theory was obtained in the fundamental case of a C*-algebra with one specified ideal by Bonkat and proved there to split, unnaturally, under certain conditions. Employing certain K-theoretical information derivable from the given operator algebras in a way 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
Cite
@article{arxiv.0801.0324,
title = {Nonsplitting in Kirchberg's ideal-related KK-theory},
author = {Soren Eilers and Gunnar Restorff and Efren Ruiz},
journal= {arXiv preprint arXiv:0801.0324},
year = {2013}
}
Comments
14 pages, minor typos fixed, 5 figures added