On the stable rank of simple C*-algebras

DOI10.1090/S0894-0347-99-00314-8zbMath0937.46052MaRDI QIDQ4257711

Jesper Villadsen

Publication date: 31 August 1999

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

stable rankreal ranknonstable \(K\)-theorysimple \(C^*\)-algebraapproximately homogeneous \(C^*\)-algebra

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) General theory of (C^*)-algebras (46L05)

Related Items (34)

Dimension growth for \(C^{*}\)-algebras ⋮ A simple \(C^ *\)-algebra with a finite and an infinite projection. ⋮ Cancellation and stable rank for direct limits of recursive subhomogeneous algebras ⋮ COVERING DIMENSION AND QUASIDIAGONALITY ⋮ Flat dimension growth for \(C^{*}\)-algebras ⋮ Subshifts and perforation ⋮ Regularity of Villadsen algebras and characters on their central sequence algebras ⋮ Decomposition rank and \(\mathcal{Z}\)-stability ⋮ The Dixmier property and tracial states for \(C^\ast\)-algebras ⋮ Nuclear dimension of simple stably projectionless \(C^\ast\)-algebras ⋮ Nuclear dimension of simple \(\mathrm{C}^*\)-algebras ⋮ 𝐶*-algebras and their nuclear dimension ⋮ The stable rank of some free product \(C^*\)-algebras ⋮ Tracial approximation in simple -algebras ⋮ Equivariant \({\mathcal{Z}} \)-stability for single automorphisms on simple \(C^*\)-algebras with tractable trace simplices ⋮ Regularity properties in the classification program for separable amenable C*-algebras ⋮ Constructing C*-diagonals in AH-algebras ⋮ The radius of comparison of the crossed product by a weakly tracially strictly approximately inner action ⋮ Simplicity, bounded normal generation, and automatic continuity of groups of unitaries ⋮ The generator rank of subhomogeneous -algebras ⋮ Covering Dimension of C*-Algebras and 2-Coloured Classification ⋮ Equivariant property (SI) revisited ⋮ On tracial approximation ⋮ Lifting \(KK\)-elements, asymptotic unitary equivalence and classification of simple C\(^*\)-algebras ⋮ The Cuntz semigroup and the radius of comparison of the crossed product by a finite group ⋮ Mean dimension and AH-algebras with diagonal maps ⋮ On topologically finite-dimensional simple \(C^*\)-algebras ⋮ AF-embeddings into \(C^*\)-algebras of real rank zero ⋮ On \(C^{\ast}\)-algebras of exponential solvable Lie groups and their real ranks ⋮ A class of simple \(C^*\)-algebras with stable rank one ⋮ The Elliott conjecture for Villadsen algebras of the first type ⋮ On invertible elements in reduced \(C^\ast\)-algebras of acylindrically hyperbolic groups ⋮ Classification of \(C^{*}\)-homomorphisms from \(C_{0}(0,1\) to a \(C^{*}\)-algebra] ⋮ Strongly self-absorbing $C^{*}$-algebras

Cites Work

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• The structure of algebras of operator fields
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• \(C^*\)-algebras of real rank zero
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• Reduction of topological stable rank in inductive limits of \(C^*\)- algebras
• Simple \(C^*\)-algebras with perforation
• The stable range of \(C^*\)-algebras
• Dimension and Stable Rank in the K -Theory of C^* -Algebras
• The Cancellation Theorem for Projective Modules Over Irrational Rotation C*-Algebras
• A Stable Cancellation Theorem for Simple C*-Algebras
• THE REAL RANK OF ALGEBRAS OF MATRIX VALUED FUNCTIONS
• The real rank of inductive limit $C^*$-algebras.
• Characteristic Classes. (AM-76)

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