Real rank of some multiplier algebras

2024/02/01 by Hannes Thiel, Thiel, Hannes · 1 citation
Computer Science · Mathematics · #46L85 #46M20 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Primary 46L05 #Rings, Modules, and Algebras #Secondary 46L80

paper · pdf · doi:10.48550/arxiv.2402.01022

openalex publication_date 2024/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there exists a separable, nuclear C*-algebra with real rank zero and trivial K-theory such that its multiplier and corona algebra have real rank one. This disproves two conjectures of Brown and Pedersen. We also compute the real rank of the stable multiplier algebra and the stable corona algebra of countably decomposable type I_∞ and type II_∞ factors. Together with results of Zhang this completes the computation of the real rank for stable multiplier and corona algebras of countably decomposable factors.

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• The Global Glimm Property for C*-algebras of topological dimension zero

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