Graphs and CCR algebras

TL;DR

This paper introduces a novel method to associate C*-algebras with graphs, resulting in a simple nuclear algebra that admits irreducible representations on both separable and nonseparable Hilbert spaces.

Contribution

It presents a new construction linking graphs to C*-algebras, expanding the understanding of their representation theory.

Findings

Constructed a simple nuclear C*-algebra from a graph

Demonstrated existence of irreducible representations on different Hilbert spaces

Provided a new perspective on CCR algebras associated with graphs

Abstract

I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.