On a family of $C^{\ast }$-subalgebras of Cuntz-Krieger algebras

Abstract

In this paper, we study a family of $C^{\ast }$-subalgebras defined by fixed points of generalized gauge actions of a Cuntz-Krieger algebra, by introducing a family of étale groupoids whose associated $C^{\ast }$-algebras are these $C^{\ast }$-subalgebras. We know that topological conjugacy classes of one-sided topological Markov shifts are characterized in terms of the isomorphism classes of these étale groupoids.

arXiv comment26 pages

References in corpus (4)

• Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras
• Flow equivalence of topological Markov shifts and Ruelle algebras
• Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts
• One-sided topological conjugacy of topological Markov shifts, continuous full groups and Cuntz--Krieger algebras

Cited by in corpus (2)

• Conjugacy of local homeomorphisms via groupoids and C*-algebras
• One-sided topological conjugacy of topological Markov shifts, continuous full groups and Cuntz--Krieger algebras