\(C^*\)-algebras of stable rank one and their Cuntz semigroups

DOI10.1215/00127094-2021-0009zbMath1490.19005arXiv1809.03984OpenAlexW4206249215MaRDI QIDQ2073278

Ramon Antoine, Hannes Thiel, Francesc Perera, Leonel Robert

Publication date: 1 February 2022

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.03984

zbMATH Keywords

\(C^*\)-algebrasemilatticeHilbert \(C^*\)-moduleCuntz semigroupstable rank oneweak comparisoninf-semilattice

Mathematics Subject Classification ID

(C^*)-modules (46L08) Classifications of (C^*)-algebras (46L35) (K_0) as an ordered group, traces (19K14)

Related Items (18)

Stable elements and property (S) ⋮ Ranks of operators in simple \(C^*\)-algebras with stable rank one ⋮ The Cuntz semigroup of unital commutative AI-algebras ⋮ A systematic approach for invariants of $C^*$-algebras ⋮ The radius of comparison of the crossed product by a weakly tracially strictly approximately inner action ⋮ The Global Glimm Property ⋮ Comparison properties for asymptotically tracially approximation \(C^*\)-algebras ⋮ Soft operators in C*-algebras ⋮ A total Cuntz semigroup for \(C^*\)-algebras of stable rank one ⋮ Simplicity, bounded normal generation, and automatic continuity of groups of unitaries ⋮ Traces on ultrapowers of \(\mathrm{C}^{*}\)-algebras ⋮ The unitary Cuntz semigroup on the classification of non-simple \(C^\ast\)-algebras ⋮ Colored isomorphism of classifiable C-algebras ⋮ Dynamical comparison and \(\mathcal{Z} \)-stability for crossed products of simple \(C^\ast \)-algebras ⋮ Tracial oscillation zero and \(\mathcal{Z}\)-stability ⋮ Nowhere scattered \(C^{\ast}\)-algebras ⋮ Malcolmson semigroups ⋮ Uniformly based Cuntz semigroups and approximate intertwinings

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