English

When universal edge-colored directed graph $C^*$-algebras are exact

Operator Algebras 2016-05-13 v3

Abstract

We consider when the universal CC^*-algebras associated to edge-colored directed graphs are exact. Specifically, for countable edge-colored directed graphs we show that the universal CC^*-algebra is exact if and only if the CC^*-algebra is isomorphic to a graph CC^*-algebra which occurs precisely when the universal and reduced CC^*-algebras of the edge-colored directed graph are isomorphic.

Keywords

Cite

@article{arxiv.1307.5801,
  title  = {When universal edge-colored directed graph $C^*$-algebras are exact},
  author = {Benton Duncan},
  journal= {arXiv preprint arXiv:1307.5801},
  year   = {2016}
}

Comments

14 pages, a complete revision which corrects errors in Propositions 1, 3, and 5 and throughout subsection 5.1 of the previous version. The errors in Propositions 3 and 5 were pointed out by an anonymous referee whose comments also significantly improved the exposition. Comments welcome

R2 v1 2026-06-22T00:55:39.249Z