Graph theoretic invariants for operator algebras associated to topological dynamics

TL;DR

This paper introduces a new graph-based invariant for classifying certain nonselfadjoint operator algebras with a conditional expectation onto a commutative diagonal, expanding the tools for algebra classification.

Contribution

It constructs an edge-colored directed graph invariant specifically for nonselfadjoint operator algebras with a conditional expectation onto a commutative diagonal.

Findings

The graph invariant helps distinguish nonselfadjoint operator algebras.

The invariant extends existing classification methods.

It provides a new perspective linking graph theory and operator algebra classification.

Abstract

We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed graph which can be used as an operator algebra invariant.