Braid groups and symplectic Steinberg groups

We construct a homomorphism $f$ from the braid group $B_{2 n + 2}$ on $2 n + 2$ strands to the Steinberg group $St (C_{n}, ℤ)$ associated with the Lie type $C_{n}$ and with integer coefficients. This homomorphism lifts the well-known symplectic representation (aka the integral Burau representation) of the braid group. We also describe the image and the kernel of $f$ .

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Keywords

braid group, Artin group, Steinberg group, symplectic modular group, group presentation

Mathematical Subject Classification

Primary: 19C09, 20F36, 20G30

Secondary: 11E57, 20F05, 22E40

Milestones

Received: 23 June 2023

Revised: 6 October 2023

Accepted: 31 October 2023

Published: 6 December 2023

Authors

François Digne
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée Université de Picardie-Jules Verne CNRS Amiens France

Christian Kassel
Institut de Recherche Mathématique Avancée, CNRS Université de Strasbourg Strasbourg France

Vol. 8, No. 4, 2023

François Digne and Christian Kassel

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors