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

Laurent Cantier

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arXiv · 2111.06926

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

Laurent Cantier

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Abstract

This paper argues that the unitary Cuntz semigroup, introduced in [10] and termed Cu$_1$, contains crucial information regarding the classification of non-simple C$^*$-algebras. We exhibit two (non-simple) C$^*$-algebras that agree on their Cuntz semigroups, termed Cu, and their K$_1$-groups and yet disagree at level of their unitary Cuntz semigroups. In the process, we establish that the unitary Cuntz semigroup contains rigorously more information about non-simple C$^*$-algebras than Cu and K$_1$ alone.

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Laurent Cantier. 2021-11-12. The unitary Cuntz semigroup on the classification of non-simple C*-algebras. https://arxiv.org/abs/2111.06926

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