Higher dimensional generalizations of the Thompson groups via higher rank graphs

TL;DR

This paper introduces a new family of groups derived from higher rank graphs, extending the concept of symmetric groups to higher dimensions, and analyzes their properties using homological invariants.

Contribution

It constructs higher-dimensional analogues of Thompson groups from higher rank graphs and develops homological invariants to distinguish these groups from existing ones.

Findings

Many groups are not isomorphic to nV for n ≥ 2

Homological invariants effectively distinguish the new groups

The groups generalize symmetric groups to higher dimensions

Abstract

We construct a family of groups from suitable higher rank graphs which are analogues of the finite symmetric groups. We introduce homological invariants showing that many of our groups are, for example, not isomorphic to $nV$, when $n \geq 2$.