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arXiv · 2109.13501

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

Mohamad N. Nasser·Mohammad N. Abdulrahim
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Abstract

Let $C_n$ be the group of conjugating automorphisms. We study the representation $\rho$ 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 $\rho$ is unfaithful for $n \geq 5$, the cases $n=3,4$ remain open. In our work, we make attempts towards the faithfulness of $\rho$ in the case $n=3$.

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Mohamad N. Nasser, Mohammad N. Abdulrahim. 2021-09-28. On The Faithfulness of the extension of Lawrence-Krammer representation of the group of conjugating automorphisms C_3. https://arxiv.org/abs/2109.13501

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