Remarks on Villadsen algebras, II: A generalized construction and the comparison radius function

2025/10/15 by George A. Elliott, Elliott, George A., Zhuang Niu +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2510.13695

openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

The authors' recent classification of Jesper Villadsen's remarkable generalization (based on a self-reproducing seed space) of Glimm's infinite tensor product (UHF) C*-algebras, by means of the Cuntz semigroup (in the case of a fixed, well-behaved, seed space), is extended to the analogous generalization of Bratteli's approximately finite-dimensional (AF) C*-algebras. Some progress is made in the direction of distinguishing between algebras based on different seed spaces.

Citations

• The Rank Ratio Function and the Radius of Comparison
• Simple AH algebras with the same Elliott invariant and radius of comparison
• Remarks on Villadsen algebras
• The Cuntz semigroup and the radius of comparison of the crossed product by a finite group
• Ranks of operators in simple C*-algebras with stable rank one
• On the classification of simple amenable C*-algebras with finite decomposition rank
• Mean dimension and AH-algebras with diagonal maps
• Recursive subhomogeneous algebras

Related

• Remarks on Villadsen algebras
• Villadsen algebras
• An algebraic approach to the radius of comparison
• Comparison Properties of the Cuntz semigroup and applications to\n C*-algebras
• The Elliott conjecture for Villadsen algebras of the first type