Rotation groups, mediangle graphs, and periagroups: a unified point of view on Coxeter groups and graph products of groups

TL;DR

This paper introduces rotation groups as a unifying framework for Coxeter groups and graph products, providing algebraic characterizations and geometric tools to analyze their properties.

Contribution

It presents rotation groups, periagroups, and mediangle graphs as a unified approach to study Coxeter groups and graph products of groups, with new algebraic and geometric insights.

Findings

Unified algebraic presentation of rotation groups and periagroups

Development of mediangle graphs for geometric analysis

Simplified proofs of known properties for Coxeter groups and graph products

Abstract

In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups (including right-angled Artin groups). We characterise algebraically these groups by presentations (periagroups) and we propose a combinatorial geometry (mediangle graphs) to study them. As an application, we give natural and unified proofs for several results that hold for both Coxeter groups and graph products of groups.