The Regular C*-algebra of an Integral Domain

Details The Regular C*-algebra of an Integral Domain The Regular C*-algebra of an Integral Domain

2008-07-09

arxiv.org/abs/0807.1407v1

Mathematics

Operator Algebras

30 pages

Scientific paper

To each integral domain R with finite quotients we associate a purely infinite simple C*-algebra in a very natural way. Its stabilization can be identified with the crossed product of the algebra of continuous functions on the "finite adele space" corresponding to R by the action of the ax+b-group over the quotient field Q(R). We study the relationship to generalized Bost-Connes systems and deduce for them a description as universal C*-algebras with the help of our construction.

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