Dyer groups (Luis Paris, Université de Bourgogne)

27.02.2024 10:30

Coxeter groups and right-angled Artin groups share the same solution to the word problem: that given by Tits for Coxeter groups and that given by Green for right-angled Artin groups. This algorithm goes beyond the simple solution to the word problem, since it allows to determine whether an expression is reduced or not, and it is an essential tool for defining normal forms in both families. Hence the question: what do these two families of groups have in common that makes them have the same solution to the word problem? The answer sits inside Dyer's thesis published in 1990 where a family of groups is described which contains both, Coxeter groups and right-angled Artin groups. We prove that all Dyer groups have this solution to the word problem and that any group which admits such a solution is a Dyer group up to a small modification of the definition. The coincidence does not stop there because these two families of groups share many other properties. This talk will be a propaganda for Dyer's groups.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 27.02.2024, Séminaire "Groupes et Géométrie"

entrée libre