Luis Paris

activity

20102026

collaborators

10 papers

math.GR2026

Smallest quotients and profinite rigidity of irreducible spherical type Artin groups

Federica Gavazzi, Igor Haladjian, Luis Paris

We prove that irreducible spherical type Artin groups are profinitely rigid within the class of all spherical type Artin groups. As part of the proof, building on ideas of Kolay fo…

math.GR2026

A cube complex for virtual Artin groups

Jos{é} Galvez Mateos, José Galvez Mateos, Luis Paris

Let $Γ$ be a Coxeter graph, and let $S$ be its vertex set. An elemental complex over $Γ$ is an abstract simplicial complex $D$ on $S$ that contains every pair ${s, t}$ w…

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…

math.GR2024

When is a TRAAG orderable?

Yago Antolín, Martín Blufstein, Luis Paris

We characterize, in terms of the defining graph, when a twisted right-angled Artin group (a group whose only relations among pairs of generators are either commuting or Klein-bottl…

math.GR2024

Intersection of Parabolic Subgroups in Euclidean Braid Groups: a short proof

María Cumplido, Federica Gavazzi, Luis Paris

We give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups $A [A ~_{n}]$ is again a p…

math.GR2020

Virtual an arrow Temperley--Lieb algebras, Markov traces, and virtual link invariants

Luis Paris, Loïc Rabenda

Let R f = Z[A $\pm$ 1 ] be the algebra of Laurent polynomials in the variable A and let R a = Z[A $\pm$ 1 , z 1 , z 2 ,. .. ] be the algebra of Laurent polynomials in the variable A…

math.GR2017

Note on residual finiteness of Artin groups

Luis Paris, Ruben Blasco-Garcia, Arye Juhasz

Let $A$ be an Artin group. A partition $P$ of the set of standard generators of $A$ is called admissible if, for all $X, Y \in P$ , $X \neq = Y$ , there is at most o…

math.GR2010

$K (π, 1)$ and word problems for infinite type Artin-Tits groups, and applications to virtual braid groups

Eddy Godelle, Luis Paris

Let $Γ$ be a Coxeter graph, let $(W, S)$ be its associated Coxeter system, and let $(A, Σ$ ) be its associated Artin-Tits system. We regard $W$ as a reflection group acting on a real…

Smallest quotients and profinite rigidity of irreducible spherical type Artin groups

A cube complex for virtual Artin groups

Classification of Artin groups admitting retractions onto their parabolic subgroups

Parabolic subgroups and word problem in virtual Artin groups

Representations of Coxeter groups over fusion rings and hyperplane complements

When is a TRAAG orderable?

Intersection of Parabolic Subgroups in Euclidean Braid Groups: a short proof

Virtual an arrow Temperley--Lieb algebras, Markov traces, and virtual link invariants

Note on residual finiteness of Artin groups

K(π,1) and word problems for infinite type Artin-Tits groups, and applications to virtual braid groups

$K (π, 1)$ and word problems for infinite type Artin-Tits groups, and applications to virtual braid groups