On the stable rank of algebras of operator fields over N-cubes

2002/03/12 by Ping Wong Ng, Ng, Ping Wong, Takahiro Sudo +1
Mathematics · #47L99 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:47L99

paper · pdf · doi:10.48550/arxiv.math/0203115

5 pages, amstex file

arxiv created 2002/03/12 · openalex publication_date 2002/03/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a unital maximal full algebra of operator fields with base space the k-cube [0,1]^k and fibre algebras, say, A_{tt ∈ [0,1]^k}. Then the stable rank of A is bounded above by the supremum of the stable ranks sr(C([0,1]^k) ⊗ A_t) for t ∈ [0,1]^k. Using this estimate, we compute the stable ranks of the universal C^*-algebras of the discrete Heisenberg groups.

Related

• On the stable rank of algebras of operator fields over metric spaces
• Ranks of operators in simple C*-algebras with stable rank one
• Unitary stable ranks and norm-one ranks
• The stable rank of some free product C*-algebras
• Stable rank for inclusions of Banach algebras