A crossed-product approach to the Cuntz-Li algebras

Steven Kaliszewski, Magnus B. Landstad, John Quigg

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)429-459
Number of pages31
JournalProceedings of the Edinburgh Mathematical Society
Volume55
Issue number2
DOIs
StatePublished - Jun 1 2012

Keywords

  • C*-crossed product
  • adele ring
  • number field

ASJC Scopus subject areas

  • Mathematics(all)

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