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

Institut for Matematiske Fag

4 Citationer (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.

Originalsprog	Engelsk
Tidsskrift	Canadian Mathematical Bulletin
Vol/bind	54
Sider (fra-til)	68-81
ISSN	0008-4395
DOI	https://doi.org/10.4153/CMB-2010-083-7
Status	Udgivet - mar. 2011

Adgang til dokumentet

10.4153/CMB-2010-083-7

Citationsformater

@article{e13a09a9eff1430abd9aec3cd80df060,

title = "Non-splitting in Kirchberg's Ideal-related KK-Theory",

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.",

author = "S{\o}ren Eilers and Gunnar Restorff and Efren Ruiz",

year = "2011",

month = mar,

doi = "10.4153/CMB-2010-083-7",

language = "English",

volume = "54",

pages = "68--81",

journal = "Canadian Mathematical Bulletin",

issn = "0008-4395",

publisher = "Canadian Mathematical Society",

}

TY - JOUR

T1 - Non-splitting in Kirchberg's Ideal-related KK-Theory

AU - Eilers, Søren

AU - Restorff, Gunnar

AU - Ruiz, Efren

PY - 2011/3

Y1 - 2011/3

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 -