Fundamental $C^*$-algebras associated to automata groups

TL;DR

This paper investigates the properties of $C^*$-algebras constructed from the fundamental actions of automaton groups on regular rooted trees, aiming to understand their algebraic and analytical structure.

Contribution

It introduces a framework for analyzing $C^*$-algebras associated with automaton groups acting on rooted trees, highlighting their fundamental properties.

Findings

Characterization of the $C^*$-algebra structure

Identification of key properties related to automaton group actions

Insights into the algebraic and topological features of these $C^*$-algebras

Abstract

We propose to study some properties of the $C^*$-algebra naturally built out of the fundamental action that an automaton group $G$ admits on a regular rooted trees $\tree$.