Diagonal-preserving gauge-invariant isomorphisms of graph C^*-algebras

Authors

Toke Meier Carlsen, University of the Faroe IslandsFollow
James Rout, University of WollongongFollow

RIS ID

115156

Publication Details

Carlsen, T. Meier. & Rout, J. (2017). Diagonal-preserving gauge-invariant isomorphisms of graph C^*-algebras. Journal of Functional Analysis, 273 (9), 2981-2993.

Abstract

We study graph C*-algebras equipped with generalised gauge actions, and characterise in terms of groupoids and groupoid cocycles when two graph C*-algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the generalised gauge actions. We apply this characterisation to show that two Cuntz-Krieger algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the gauge actions if and only if the corresponding one-sided subshifts are eventually conjugate, and that the stabilisation of two Cuntz-Krieger algebras are isomorphic by a diagonal-preserving isomorphism that intertwines the gauge actions if and only if the corresponding two-sided subshifts are conjugate.