Strong classification of extensions of classifiable $C^{*}$-algebras

S{\o}ren Eilers; Gunnar Restorff; Efren Ruiz

doi:10.4134/BKMS.b210047

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2022; 59(3): 567-608

Online first article May 11, 2022 Printed May 31, 2022

https://doi.org/10.4134/BKMS.b210047

Strong classification of extensions of classifiable $C^{*}$-algebras

S{\o}ren Eilers, Gunnar Restorff, Efren Ruiz

Universitetsparken~5; FO-100 T\'orshavn; Hilo, Hawaii

Abstract

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Abstract

We show that certain extensions of classifiable $C^{*}$-algebras are strongly classified by the associated six-term exact sequence in $K$-theory together with the positive cone of $K_{0}$-groups of the ideal and quotient. We use our results to completely classify all unital graph $C^{*}$-algebras with exactly one non-trivial ideal.

Keywords: Classification, extensions, graph algebras

MSC numbers: Primary 46L35