Intersection of parabolic subgroups in Euclidean braid groups: a short proof
We give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups $A[\tilde{A}_n]$ is again a parabolic subgroup. To that end, we use that the spherical-type Artin group $A[B_{n+1}]$ is isomorphic to $A[\tilde{A}_n]...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.656/ |
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| author | Cumplido, María Gavazzi, Federica Paris, Luis |
| author_facet | Cumplido, María Gavazzi, Federica Paris, Luis |
| author_sort | Cumplido, María |
| collection | DOAJ |
| description | We give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups $A[\tilde{A}_n]$ is again a parabolic subgroup. To that end, we use that the spherical-type Artin group $A[B_{n+1}]$ is isomorphic to $A[\tilde{A}_n]\rtimes \mathbb{Z}$ . |
| format | Article |
| id | doaj-art-0514bc876a61473687115b50942de01d |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-0514bc876a61473687115b50942de01d2025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111445144810.5802/crmath.65610.5802/crmath.656Intersection of parabolic subgroups in Euclidean braid groups: a short proofCumplido, María0Gavazzi, Federica1Paris, Luis2Departamento de Álgebra, Facultad de Matemáticas, Universidad de Sevilla, Calle Tarfia s/n 41012, Seville, SpainIMB, UMR5584, CNRS, Université de Bourgogne, 21000 Dijon, FranceIMB, UMR5584, CNRS, Université de Bourgogne, 21000 Dijon, FranceWe give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups $A[\tilde{A}_n]$ is again a parabolic subgroup. To that end, we use that the spherical-type Artin group $A[B_{n+1}]$ is isomorphic to $A[\tilde{A}_n]\rtimes \mathbb{Z}$ .https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.656/Group theoryArtin groupsEuclidean braid groupsparabolic subgroupsgroup isomorphism |
| spellingShingle | Cumplido, María Gavazzi, Federica Paris, Luis Intersection of parabolic subgroups in Euclidean braid groups: a short proof Comptes Rendus. Mathématique Group theory Artin groups Euclidean braid groups parabolic subgroups group isomorphism |
| title | Intersection of parabolic subgroups in Euclidean braid groups: a short proof |
| title_full | Intersection of parabolic subgroups in Euclidean braid groups: a short proof |
| title_fullStr | Intersection of parabolic subgroups in Euclidean braid groups: a short proof |
| title_full_unstemmed | Intersection of parabolic subgroups in Euclidean braid groups: a short proof |
| title_short | Intersection of parabolic subgroups in Euclidean braid groups: a short proof |
| title_sort | intersection of parabolic subgroups in euclidean braid groups a short proof |
| topic | Group theory Artin groups Euclidean braid groups parabolic subgroups group isomorphism |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.656/ |
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