On nuclearity and exactness of the tame C*-algebras associated with finitely separated graphs

TL;DR

This paper introduces a new graph property called Condition (N) for finitely separated graphs and proves it characterizes the nuclearity and exactness of their associated tame C*-algebras.

Contribution

The paper establishes the equivalence between Condition (N) and key C*-algebra properties, providing a graph-theoretic criterion for nuclearity and exactness.

Findings

Condition (N) is equivalent to nuclearity of the associated C*-algebra.

Condition (N) is equivalent to exactness of the associated C*-algebra.

Provides a graph-theoretic characterization of C*-algebra properties.

Abstract

We introduce a graph theoretic property called Condition (N) for finitely separated graphs and prove that it is equivalent to both nuclearity and exactness of the associated universal tame graph C*-algebra.