On The Faithfulness of the extension of Lawrence-Krammer representation of the group of conjugating automorphisms C_3

Mohamad N. Nasser; Mohammad N. Abdulrahim

paper

On The Faithfulness of the extension of Lawrence-Krammer representation of the group of conjugating automorphisms C_3

arXiv:2109.13501

Abstract

Let $C_{n}$ be the group of conjugating automorphisms. We study the representation $ρ$ of $C_{n}$ , an extension of Lawrence-Krammer representation of the braid group $B_{n}$ , defined by Valerij G. Bardakov. As Bardakov proved that the representation $ρ$ is unfaithful for $n \geq 5$ , the cases $n = 3, 4$ remain open. In our work, we make attempts towards the faithfulness of $ρ$ in the case $n = 3$ .

References in corpus (1)

The structure of the group of conjugating automorphisms and the linear representation of the braid groups of some manifolds