The Regular C*-algebra of an Integral Domain

By J. Cuntz, Xin Li. 2008

65 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e1b5fcd321235826f54665bd9434d4897e372bb4

How researchers see this paper

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In Algebra and Number Theory

1. Xin Li
2. J. Cuntz
3. S. Echterhoff
4. Nathan Brownlowe
5. Michael F. Whittaker
6. Jacqui Ramagge
7. D. Robertson

In Applied Mathematics

1. Xin Li
2. S. Echterhoff

In Mathematical Physics

1. Xin Li
2. J. Cuntz
3. S. Echterhoff
4. Nathan Brownlowe
5. Michael F. Whittaker
6. Jacqui Ramagge
7. D. Robertson
8. Charles Starling

Citations in the corpus

• On the K-theory of crossed products by automorphic semigroup actions (2012, background): “[11] the second one admits a largest ideal (which contains any other non-trivial ideal) with a simple quotient (the ring C*-algebra of [8])).”
• Zappa-Sz\'ep products of semigroups and their C*-algebras (2013, background): “In [5] Cuntz also introduced the C-algebra QZ, which instigated work on the C-algebras of more general integral domains [7].”