Mathematics – Operator Algebras
Scientific paper
2010-10-05
Mathematics
Operator Algebras
11 pages
Scientific paper
Recently, Cuntz and Li introduced the C^*-algebra A[R] associated to an integral domain R with finite quotients. In this paper, we show that A[R] is a partial group algebra of the group $K \rtimes K^x$ with suitable relations, where K is the field of fractions of R. We identify the spectrum of this relations and we show that it is homeomorphic to the profinite completion of R. By using partial crossed product theory, we reconstruct some results proved by Cuntz and Li. Among them, we prove that $\ar$ is simple by showing that the action is topologically free and minimal.
Boava Giuliano
Exel Ruy
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