- journal article metadata
European Mathematical Society Publishing House
2018-03-26 23:30:00
Journal of Noncommutative Geometry
J. Noncommut. Geom.
JNCG
1661-6952
1661-6960
Global analysis, analysis on manifolds
General
10.4171/JNCG
http://www.ems-ph.org/doi/10.4171/JNCG
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
12
2018
1
Automorphisms of Cuntz–Krieger algebras
Søren
Eilers
University of Copenhagen, Denmark
Gunnar
Restorff
University of the Faroe Islands, Tórshavn, Faroe Islands
Efren
Ruiz
University of Hawaii, Hilo, USA
KK-theory, UCT, Cuntz–Krieger algebras, automorphisms
We prove that the natural homomorphism from Kirchberg’s ideal-related $KK$-theory, $KK_\mathcal E(e, e')$, with one specified ideal, into $\mathrm{Hom}_{\Lambda} (\ushort{K}_{\mathcal{E}} (e), \ushort{K}_{\mathcal{E}} (e'))$ is an isomorphism for all extensions $e$ and $e'$ of separable, nuclear $C^{*}$-algebras in the bootstrap category $\mathcal{N}$ with the $K$-groups of the associated cyclic six term exact sequence being finitely generated, having zero exponential map and with the $K_{1}$-groups of the quotients being free abelian groups. This class includes all Cuntz–Krieger algebras with exactly one non-trivial ideal. Combining our results with the results of Kirchberg, we classify automorphisms of the stabilized purely infinite Cuntz–Krieger algebras with exactly one non-trivial ideal modulo asymptotically unitary equivalence. We also get a classification result modulo approximately unitary equivalence. The results in this paper also apply to certain graph algebras.
Functional analysis
217
254
10.4171/JNCG/275
http://www.ems-ph.org/doi/10.4171/JNCG/275
3
23
2018