Braid groups are linear groups
type: Item
instance of: scholarly article
title: Braid groups are linear groups
zbMATH Open document ID: 0879.20016
published in: Advances in Mathematics
publication date: 1997-11-26T00:00:00Z
review text: Let \(B_n\) denote the braid group on \(n\) strings. \(B_2\) is infinite cyclic and hence is a linear group. It is well-known that \(B_3\) is also a linear group. But it has remained an open problem as to whether any other braid groups are linear. In 1936 Burau gave a matrix representation of \(B_n\) and in 1961 Gassner generalized Burau's representation. The author shows that \(B_n\) is linear for all \(n\) by proving Theorem A. The Gassner representation of \(B_n\) is faithful for every \(n\).
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 934290
zbMATH Keywords: braid groups
zbMATH Keywords: faithfulness of Gassner representations
zbMATH Keywords: free groups of finite rank
zbMATH Keywords: linear groups
author: Seymour Bachmuth
reviewed by: V. M. Levchuk
MaRDI profile type: Publication
full work available at URL: aima.1996.0046
OpenAlex ID: W2073004814
DOI: 10.1006/AIMA.1996.0046
description: scientific article; zbMATH DE number 934290