Gauge-invariant uniqueness theorems for $P$-graphs

TL;DR

This paper establishes gauge-invariant uniqueness theorems for $P$-graph $C^*$-algebras using maximal coactions, offering a more natural framework than previous normal coaction-based approaches.

Contribution

It introduces a new approach to gauge-invariant uniqueness theorems for $P$-graph $C^*$-algebras utilizing maximal coactions instead of normal coactions.

Findings

Maximal coactions provide a natural basis for uniqueness theorems.

Characterization of co-universal representations for Fell bundles.

Abstract framework applicable to $P$-graph $C^*$-algebras.

Abstract

We prove a version of the result in the title that makes use of maximal coactions in the context of discrete groups. Earlier Gauge-Invariant Uniqueness theorems for $C^*$-algebras associated to $P$-graphs and similar $C^*$-algebras exploited a property of coactions known as normality. In the present paper, the view point is that maximal coactions provide a more natural starting point to state and prove such uniqueness theorems. A byproduct of our approach consists of an abstract characterization of co-universal representations for a Fell bundle over a discrete group.