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A crossed-product approach to the Cuntz–Li algebras

Part of: Algebraic number theory: global fields Selfadjoint operator algebras

Published online by Cambridge University Press:  12 April 2012

S. Kaliszewski ,
Magnus B. Landstad  and
John Quigg
S. Kaliszewski
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287 (quigg@asu.edu; kaliszewski@asu.edu)
Magnus B. Landstad
Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway (magnusla@math.ntnu.no)
John Quigg
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287 (quigg@asu.edu; kaliszewski@asu.edu)
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Abstract

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Cuntz and Li have defined a C*-algebra associated to any integral domain, using generators and relations, and proved that it is simple and purely infinite and that it is stably isomorphic to a crossed product of a commutative C*-algebra. We give an approach to a class of C*-algebras containing those studied by Cuntz and Li, using the general theory of C*-dynamical systems associated to certain semidirect product groups. Even for the special case of the Cuntz–Li algebras, our development is new.

Keywords

C*-crossed productnumber fieldadele ring

MSC classification

Secondary: 46L55: Noncommutative dynamical systems 46L05: General theory of $C^*$-algebras 11R04: Algebraic numbers; rings of algebraic integers 11R56: Adèle rings and groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 2 , June 2012 , pp. 429 - 459
Copyright
Copyright © Edinburgh Mathematical Society 2012

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