Amplified graph C*-algebras II: Reconstruction

Abstract

Let E E be a countable directed graph that is amplified in the sense that whenever there is an edge from v v to w w , there are infinitely many edges from v v to w w . We show that E E can be recovered from C ∗ ( E ) C^*(E) together with its canonical gauge-action, and also from L K ( E ) L_\mathbb {K}(E) together with its canonical grading.