Partial crossed product description of the C*-algebras associated with\n integral domains

2010/10/05 by Giuliano Boava, Boava, Giuliano, Ruy Exel +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1010.0967

openalex publication_date 2010/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Cuntz and Li introduced the C^*-algebra A[R] associated to an\nintegral domain R with finite quotients. In this paper, we show that A[R] is a\npartial group algebra of the group K rtimes K^x with suitable relations,\nwhere K is the field of fractions of R. We identify the spectrum of this\nrelations and we show that it is homeomorphic to the profinite completion of R.\nBy using partial crossed product theory, we reconstruct some results proved by\nCuntz and Li. Among them, we prove that ar is simple by showing that the\naction is topologically free and minimal.\n

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