The interplay between linear representations of the braid group.
type: Item
instance of: scholarly article
title: The interplay between linear representations of the braid group.
zbMATH Open document ID: 1140.20031
DOI: 10.1155/2007/16186
author: Mohammad N. Abdulrahim
author: Nibal H. Kassem
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-06-03T00:00:00Z
full work available at URL: https://eudml.org/doc/54291
review text: Summary: We consider Wada's representation as a twisted version of the standard action of the braid group, \(B_n\), on the free group with \(n\) generators. Constructing a free group, \(G_{nm}\), of rank \(nm\), we compose Cohen's map \(B_n\to B_{nm}\) and the embedding \(B_{nm}\to\Aut(G_{nm})\) via Wada's map. We prove that the composition factors of the obtained representation are one copy of Burau representation and \(m-1\) copies of the standard representation after changing the parameter \(t\) to \(t^k\) in the definitions of the Burau and standard representations. This is a generalization of our previous result concerning the standard Artin representation of the braid group.
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 5282522
zbMATH Keywords: Artin representation
zbMATH Keywords: braid groups
zbMATH Keywords: Burau representation
zbMATH Keywords: Wada representation
MaRDI profile type: Publication
OpenAlex ID: W2074497659
cites work: Q5522902
cites work: Q3699000
cites work: REPRESENTING BRAIDS BY AUTOMORPHISMS
cites work: Generalizations of the standard Artin representation are unitary.
cites work: Dimension \(n\) representations of the braid group on \(n\) strings
cites work: ON THE COMPOSITION OF THE BURAU REPRESENTATION AND THE NATURAL MAP Bn → Bnk
cites work: Braids, Links, and Mapping Class Groups. (AM-82)
description: scientific article; zbMATH DE number 5282522