2019/05/23 by Kazunori Kodaka, Kodaka, Kazunori
Mathematics · #46L05 (Primary) #46L08 (Secondary) #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L05 #msc:46L08
paper · pdf · doi:10.48550/arxiv.1905.10001
26 pages, We repaired some mistakes
openalex publication_date 2019/05/23 · arxiv created 2019/10/09 · arxiv updated 2019/10/10 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
Let A= \At \t ∈ G and B= \Bt \t∈ G be C^*-algebraic bundles over a finite group G. Let C=⊕t ∈ GAt and D=⊕t∈ GBt. Also, let A=Ae and B=Be, where e is the unit element in G. We suppose that C and D are unital and A and B have the unit elements in C and D, respectively. In this paper, we shall show that if there is an equivalence A-B-bundle over G with some properties, then the unital inclusions of unital C^*-algebras A ⊂ C and B ⊂ D induced by A and B are strongly Morita equivalent. Also, we suppose that A and B are saturated and that A' ∩ C= C 1. We shall show that if A ⊂ C and B ⊂ D are strongly Morita equivalent, then there are an automorphism f of G and an equivalence bundle A-Bf -bundle over G with the some properties, where Bf is the C^*-algebraic bundle induced by B and f, which is defined by Bf = \Bf(t) \t ∈ G. Furthermore, we shall give an application.