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

María Cumplido; Federica Gavazzi; Luis Paris

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

Group Theory 2024-02-20 v1

Authors: María Cumplido , Federica Gavazzi , Luis Paris

Abstract

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 $A[\tilde{A}_n] \rtimes \mathbb{Z}$ .

Keywords

braid groups hyperbolic groups

Cite

@article{arxiv.2402.10919,
  title  = {Intersection of Parabolic Subgroups in Euclidean Braid Groups: a short proof},
  author = {María Cumplido and Federica Gavazzi and Luis Paris},
  journal= {arXiv preprint arXiv:2402.10919},
  year   = {2024}
}

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3 pages, 2 figures

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

Abstract

Keywords

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