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Research Article Open access CC BY 3.0

A New Six Dimensional Representation of the Braid Group on Three Strands and its Irreducibility and Unitarizability

Madline A. Al-Tahan, Mohammad N. Abdulrahim

Journal of Advances in Mathematics and Computer Science · pp. 275–280 · Published 29 Apr 2013

10.9734/BJMCS/2013/3141

Abstract

We consider the braid group on three strands, B3and construct a complex valued representation of it with degree 6, namely,  First, we show that this representation is irreducible and not equivalent to either Burau or Krammer’s representations. Second, we prove that the representation is unitary relative to an invertible hermitian matrix.

Krammer’s representation Artin representation braid group Hecke algebra

Cited by 5

On a class of unitary representations of the braid groups B3 and B4

S. Albeverio, Slavik Rabanovich · Bulletin des Sciences Mathématiques · 2019

ON THE IRREDUCIBLITY OF THE REPRESENTATION OF THE PURE BRAID GROUP ON THREE STRANDS

Hasan A. Haidar, M. Abdulrahim · International Journal of Apllied Mathematics · 2019

On a special single-power cyclic hypergroup and its automorphisms

M. Al Tahan, B. Davvaz · Discret. Math. Algorithms Appl. · 2016

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