The unitary Cuntz semigroup on the classification of non-simple\n C*-algebras

2021/11/12 by Laurent Cantier, Cantier, Laurent
Mathematics · Computer Science · #Advanced Operator Algebra Research #Functional Equations Stability Results #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2111.06926

Abstract

This paper argues that the unitary Cuntz semigroup, introduced in [10] and\ntermed Cu₁, contains crucial information regarding the classification of\nnon-simple C^*-algebras. We exhibit two (non-simple) C^*-algebras that\nagree on their Cuntz semigroups, termed Cu, and their K₁-groups and yet\ndisagree at level of their unitary Cuntz semigroups. In the process, we\nestablish that the unitary Cuntz semigroup contains rigorously more information\nabout non-simple C^*-algebras than Cu and K₁ alone.\n

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