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arXiv · 2402.10919

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

María Cumplido·Federica Gavazzi·Luis Paris
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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 $A[\tilde{A}_n] \rtimes \mathbb{Z}$.

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María Cumplido, Federica Gavazzi, Luis Paris. 2024-01-24. Intersection of Parabolic Subgroups in Euclidean Braid Groups: a short proof. https://arxiv.org/abs/2402.10919

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