A crossed-product approach to the Cuntz-Li algebras

Abstract

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.

Major revision and rearrangement; split Section 6 in order to use the generators and relations from Section 9 in a better way

References in corpus (5)

• The Regular C*-algebra of an Integral Domain
• The 2-adic ring $C^{\ast }$-algebra of the integers and its representations
• Dilations of semigroup crossed products as crossed products of dilations
• Partial crossed product description of the C*-algebras associated with integral domains
• Operator algebras associated to integral domains