The regular C*-algebra of an integral domain

Cuntz, J. and Li, X. (2010) The regular C*-algebra of an integral domain. In: Blanchard, E., Ellwood, D., Khalkhali, M., Marcolli, M., Moscovici, H. and Popa, S. (eds.) Quanta of Maths: Conference in Honor of Alain Connes, Non Commutative Geometry, Institut Henri Poincaré, Institut des Hautes Études Scientifiques, Institut de Mathématiques de Jussieu, Paris, France, March 29-April 6, 2007. Series: Clay mathematics proceedings (11). American Mathematical Society ; Clay Mathematics Institute: Providence, R.I ; Cambridge, MA, pp. 149-170. ISBN 9780821852033

Abstract

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.

• Item Type: Book Sections
• Status: Published
• Glasgow Author(s) Enlighten ID: Li, Professor Xin
• Authors: Cuntz, J., and Li, X.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Publisher: American Mathematical Society ; Clay Mathematics Institute
• ISBN: 9780821852033