Some remarks about the faithfulness of the Burau representation of Artin–Tits groups
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 {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 .
Authors
- Asilata Bapat (ORCID: https://orcid.org/0000-0002-7218-5281)
- Hoel Queffélec (ORCID: https://orcid.org/0000-0002-8087-8256)
Institutions
- Australian National University (AU)
- Centre National de la Recherche Scientifique (FR)
- Université de Montpellier (FR)
- Australian Mathematical Sciences Institute (AU)
- Australian Centre for International Agricultural Research (AU)
Publication Details
- Journal
- Groups Geometry and Dynamics
- Published
- 2026-06-30
- DOI
- https://doi.org/10.4171/ggd/973
- Primary Topic
- Geometric and Algebraic Topology
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00