COMPLETIONS OF MONOIDS WITH APPLICATIONS TO THE CUNTZ SEMIGROUP

DOI10.1142/S0129167X11007057zbMath1239.46042arXiv1003.2874MaRDI QIDQ3021615

Joan Bosa, Francesc Perera, Ramon Antoine

Publication date: 26 July 2011

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.2874

zbMATH Keywords

classificationcompletionsCuntz semigroupElliott invariant

Mathematics Subject Classification ID

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

Related Items

The Cuntz semigroup, a Riesz type interpolation property, comparison and the ideal property ⋮ A bivariant theory for the Cuntz semigroup ⋮ Strict comparison for \(C^*\)-algebras arising from almost finite groupoids ⋮ Open projections and suprema in the Cuntz semigroup ⋮ The Cuntz semigroup and domain theory ⋮ The corona algebra of the stabilized Jiang-Su algebra ⋮ Nuclear dimension and 𝒵-stability of non-simple 𝒞*-algebras ⋮ Geometric structure of dimension functions of certain continuous fields ⋮ Tensor products and regularity properties of Cuntz semigroups ⋮ Closed convex hulls of unitary orbits in \({C^{\ast}_{r}(\mathbb{F}_{\infty})}\) ⋮ Recovering the Elliott invariant from the Cuntz semigroup ⋮ Classification of inductive limits of 1-dimensional NCCW complexes ⋮ Cuntz semigroups of compact-type Hopf C\(^\ast\)-algebras ⋮ The \(\alpha\)-comparison property and finite nuclear dimension of generalized inductive limits for \(C^*\)-algebras ⋮ \(C^*\)-algebras of stable rank one and their Cuntz semigroups

Cites Work

• Infinite non-simple \(C\)*-algebras: absorbing the Cuntz algebra \({\mathcal O}_\infty\)
• Flat dimension growth for \(C^{*}\)-algebras
• On the structure of simple \(C^*\)-algebras tensored with a UHF-algebra. II
• Dimension functions on simple \(C^*\)-algebras
• Recasting the Elliott conjecture
• On the classification problem for nuclear \(C^*\)-algebras
• Purely infinite corona algebras of simple C\(^*\)-algebras
• The Structure of Positive Elements for C*-Algebras with Real Rank Zero
• Non-simple purely infinite C*-algebras
• THE STABLE AND THE REAL RANK OF ${\mathcal Z}$-ABSORBING C*-ALGEBRAS
• Stability in the Cuntz semigroup of a commutative C*-algebra