2017/07/16 by Ja A Jeong, Jeong, Ja A, Gi Hyun Park +1
Mathematics · #46L05 #46L55 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1707.05703
openalex publication_date 2017/07/16 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
By a labeled graph C^*-algebra we mean a C^*-algebra associated to a\nlabeled space (E, mathcal L, mathcal E) consisting of a labeled graph\n(E, mathcal L) and the smallest normal accommodating set mathcal E of\nvertex subsets. Every graph C^*-algebra C^*(E) is a labeled graph\nC^*-algebra and it is well known that C^*(E) is simple if and only if the\ngraph E is cofinal and satisfies Condition (L). Bates and Pask extend these\nconditions of graphs E to labeled spaces, and show that if a set-finite and\nreceiver set-finite labeled space (E, mathcal L, mathcal E) is cofinal and\ndisagreeable, then its C^*-algebra C^*(E, mathcal L, mathcal E) is simple.\nIn this paper, we show that the converse is also true.\n