English

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

Operator Algebras 2018-03-02 v1

Abstract

We characterize when there exists a diagonal preserving *-isomorphism between two graph CC^*-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 EE and FF and show that this is a necessary and sufficient condition for the existence of a diagonal preserving *-isomorphism between the graph CC^*-algebras C(E)C^*(E) and C(F)C^*(F).

Keywords

Cite

@article{arxiv.1605.01202,
  title  = {A dynamical characterization of diagonal preserving $*$-isomorphisms of graph $C^*$-algebras},
  author = {Sara E. Arklint and Søren Eilers and Efren Ruiz},
  journal= {arXiv preprint arXiv:1605.01202},
  year   = {2018}
}