Amplified graph C*-algebras II: reconstruction

TL;DR

This paper demonstrates that amplified directed graphs can be uniquely reconstructed from their associated C*-algebras and gauge actions, highlighting a deep connection between graph structure and algebraic invariants.

Contribution

It establishes a reconstruction theorem for amplified graphs from their C*-algebras and graded algebras, extending previous results to a broader class of graphs.

Findings

Amplified graphs are uniquely recoverable from their C*-algebras with gauge action.

Reconstruction also possible from the associated Leavitt path algebra with grading.

Provides a method to recover graph structure from algebraic data.

Abstract

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