A crossed-product approach to the Cuntz-Li algebras

2010/12/23 by Kaliszewski, S., Landstad, M., Quigg, John
#11R04 #11R56 (Secondary) #46L05 (Primary) #46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1012.5285

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.

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