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A dynamical characterization of diagonal-preserving $^{\ast }$-isomorphisms of graph $C^{\ast }$-algebras

Published online by Cambridge University Press:  02 May 2017

SARA E. ARKLINT ,
SØREN EILERS  and
EFREN RUIZ
SARA E. ARKLINT
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark email arklint@math.ku.dk, eilers@math.ku.dk
SØREN EILERS
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark email arklint@math.ku.dk, eilers@math.ku.dk
EFREN RUIZ
Affiliation:
Department of Mathematics, University of Hawaii, Hilo, 200 W. Kawili Street, Hilo, Hawaii, 96720-4091, USA email ruize@hawaii.edu
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Abstract

We characterize when there exists a diagonal-preserving $\ast$-isomorphism between two graph $C^{\ast }$-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of ‘orbit equivalence’ between the boundary path spaces of the directed graphs $E$ and $F$ and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving $\ast$-isomorphism between the graph $C^{\ast }$-algebras $C^{\ast }(E)$ and $C^{\ast }(F)$.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 7 , October 2018 , pp. 2401 - 2421
Copyright
© Cambridge University Press, 2017 

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