Braid groups and symplectic Steinberg groups
Group Theory
2023-12-06 v5 Geometric Topology
Abstract
We construct a homomorphism from the braid group on strands to the Steinberg group associated with the Lie type and with integer coefficients. This homomorphism lifts the well-known symplectic representation of the braid groups. We also describe the image and the kernel of .
Keywords
Cite
@article{arxiv.2201.07153,
title = {Braid groups and symplectic Steinberg groups},
author = {François Digne and Christian Kassel},
journal= {arXiv preprint arXiv:2201.07153},
year = {2023}
}
Comments
21 pages. The statement and proof of Theorem 5.7 have been corrected in Version 2. Sections 5.4 and 6 were added in Version 3. Remark 5.9 added in Version 4. In Version 5: slight changes in introduction, Section 4 and acknowledgement; two references added