collaborators

4 papers

math.GR2026

A cube complex for virtual Artin groups

Jos{é} Galvez Mateos, Luis Paris

Let be a Coxeter graph, and let be its vertex set. An elemental complex over is an abstract simplicial complex on that contains every pair …

math.GR2026

Classification of Artin groups admitting retractions onto their parabolic subgroups

Bruno Aarón Cisneros de la Cruz, María Cumplido, Islam Foniqi +1

We classify the Artin groups that admit retractions onto all of their parabolic subgroups. Our approach relies on a detailed analysis of triangular subgroups, with a key ingredient…

math.GR2026

Parabolic subgroups and word problem in virtual Artin groups

José Gálvez Mateos, Federica Gavazzi, Luis Paris

We begin by establishing two fundamental results on standard parabolic subgroups of virtual Artin groups. We first show that a standard parabolic subgroup is naturally isomorphic t…

math.GR2025

Representations of Coxeter groups over fusion rings and hyperplane complements

Edmund Heng, Luis Paris

We study faithful realisations of Coxeter groups over fusion rings and study Vinberg systems associated to them. We show that they induce embeddings of hyperplane complements, whic…