Associative spectra of graph algebras II. Satisfaction of bracketing identities, spectrum dichotomy

TL;DR

This paper characterizes when a graph algebra satisfies a bracketing identity and reveals that its associative spectrum is either constant or grows exponentially.

Contribution

It provides a necessary and sufficient condition for satisfaction of bracketing identities and establishes a spectrum dichotomy for graph algebras.

Findings

Graph algebras satisfy bracketing identities under specific conditions.

Associative spectrum is either constant or exponentially growing.

Spectrum dichotomy applies to all graph algebras.

Abstract

A necessary and sufficient condition is presented for a graph algebra to satisfy a bracketing identity. The associative spectrum of an arbitrary graph algebra is shown to be either constant or exponentially growing.