On the Simplicity of C$^*$-algebras Associated to Multispinal Groups

TL;DR

This paper characterizes when the universal C*-algebra from multispinal groups is simple, showing that a matrix invertibility condition fully determines simplicity.

Contribution

It introduces a complete characterization of simplicity for C*-algebras from multispinal groups based on matrix invertibility.

Findings

Simplicity of the algebra is equivalent to a specific matrix being invertible.

Provides a clear criterion for simplicity in terms of algebraic properties.

Advances understanding of the structure of C*-algebras from multispinal groups.

Abstract

We characterize the simplicity of universal C$^*$-algebras arising from multispinal groups. Let $\mathcal{O}_{G_{\max}}$ be the universal C$^*$-algebra associated to a multispinal group $G$. We show that the invertibility of a matrix completely determines the simplicity of $\mathcal{O}_{G_{\max}}$.