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arXiv · 1605.01202

A dynamical characterization of diagonal preserving $*$-isomorphisms of graph $C^*$-algebras

Sara E. Arklint·Søren Eilers·Efren Ruiz
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Abstract

We characterize when there exists a diagonal preserving $*$-isomorphism between two graph $C^*$-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 $*$-isomorphism between the graph $C^*$-algebras $C^*(E)$ and $C^*(F)$.

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Sara E. Arklint, Søren Eilers, Efren Ruiz. 2016-05-04. A dynamical characterization of diagonal preserving $*$-isomorphisms of graph $C^*$-algebras. https://arxiv.org/abs/1605.01202

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