2011/01/25 by Ja A Jeong, Jeong, Ja A, Sun Ho Kim +1 · 1 citation
Mathematics · #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05
paper · pdf · doi:10.48550/arxiv.1101.4739
15 pages, contains minor corrections to the version submitted
arxiv created 2011/01/25 · openalex publication_date 2011/01/25 · arxiv updated 2011/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the simplicity of the C^*-algebra associated to a labelled space (E,\CL,\bE), where (E,\CL) is a labelled graph and \bE is the smallest accommodating set containing all generalized vertices. We prove that if C^*(E, \CL, \bE) is simple, then (E, \CL, \bE) is strongly cofinal, and if, in addition, \v\∈ \bE for every vertex v, then (E, \CL, \bE) is disagreeable. It is observed that C^*(E, \CL, \bE) is simple whenever (E, \CL, \bE) is strongly cofinal and disagreeable, which is recently known for the C^*-algebra C^*(E, \CL, \CEa) associated to a labelled space (E, \CL, \CEa) of the smallest accommodating set \CEa.