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

Søren Eilers|Gunnar Restorff|Efren Ruiz
대한수학회 (The Korean Mathematical Society)|2022.05|대한수학회보 (Bulletin of the KMS)|제59권 제3호|pp. 567-608|DOI 10.4134/BKMS.b210047

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참고문헌

키워드

Classificationextensionsgraph algebras
주제분류수학

초록

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.

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.

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