Artículo
Parabolic subgroups of large-type Artin groups
Autor/es | Cumplido Cabello, María
Martin, Alexandre Vaskou, Nicolás |
Departamento | Universidad de Sevilla. Departamento de Álgebra |
Fecha de publicación | 2022-09-12 |
Fecha de depósito | 2023-04-19 |
Publicado en |
|
Resumen | We show that the geometric realisation of the poset of proper parabolic subgroups of a large-type Artin group has a systolic geometry. We use this geometry to show that the set of parabolic subgroups of a large-type Artin ... We show that the geometric realisation of the poset of proper parabolic subgroups of a large-type Artin group has a systolic geometry. We use this geometry to show that the set of parabolic subgroups of a large-type Artin group is stable under arbitrary intersections and forms a lattice for the inclusion. As an application, we show that parabolic subgroups of large-type Artin groups are stable under taking roots and we completely characterise the parabolic subgroups that are conjugacy stable. We also use this geometric perspective to recover and unify results describing the normalisers of parabolic subgroups of large-type Artin groups. |
Cita | Cumplido Cabello, M., Martin, A. y Vaskou, N. (2022). Parabolic subgroups of large-type Artin groups. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 174 (2), 393-414. https://doi.org/10.1017/S0305004122000342. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
parabolic-subgroups-of-large-t ... | 412.9Kb | [PDF] | Ver/ | |