Universal operator algebras of directed graphs

TL;DR

This paper introduces universal operator algebras for directed graphs, exploring their structural properties, decomposition, continuity, and K-theoretic aspects, advancing the mathematical understanding of graph-based operator algebras.

Contribution

It defines a new class of universal operator algebras for directed graphs and analyzes their structural and K-theoretic properties, including free product decomposition and limit continuity.

Findings

Established free product decomposition of the algebras

Proved continuity of the construction with respect to direct limits

Derived K-theoretic results for the algebras

Abstract

We define and investigate properties of universal operator algebras of directed graphs. Results include free products decomposition and continuity of the construction with respect to direct limits. Lastly we prove some K-theoretic results about our algebras.