Some remarks about the faithfulness of the Burau representation of Artin--Tits groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909302111862784 |
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| author | Bapat, Asilata Queffelec, Hoel |
| author_facet | Bapat, Asilata Queffelec, Hoel |
| contents | We discuss the extension of the faithfulness question for the Burau representation of braid groups to the case of Artin--Tits groups. We prove that the Burau representation is not faithful in affine type $\tilde{A_3}$, and not faithful over several finite rings in type $D_4$, using an algorithmic approach based on categorical methods that generalize Bigelow's curve strategy outside of type $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some remarks about the faithfulness of the Burau representation of Artin--Tits groups Bapat, Asilata Queffelec, Hoel Representation Theory Group Theory Geometric Topology 20F36, 18G80, 18N25 We discuss the extension of the faithfulness question for the Burau representation of braid groups to the case of Artin--Tits groups. We prove that the Burau representation is not faithful in affine type $\tilde{A_3}$, and not faithful over several finite rings in type $D_4$, using an algorithmic approach based on categorical methods that generalize Bigelow's curve strategy outside of type $A$. |
| title | Some remarks about the faithfulness of the Burau representation of Artin--Tits groups |
| topic | Representation Theory Group Theory Geometric Topology 20F36, 18G80, 18N25 |
| url | https://arxiv.org/abs/2409.00144 |