Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc.

Published online May 11, 2022

Copyright © The Korean Mathematical Society.

Strong Classification of Extensions of Classifiable $C^*$-algebras

Søren Eilers, Gunnar Restorff, and Efren Ruiz

University of Copenhagen, University of the Faroe Islands, University of Hawaii, Hilo

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: 46L35

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