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On The Faithfulness of the extension of Lawrence-Krammer representation of the group of conjugating automorphisms C₃
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On The Faithfulness of the extension of Lawrence-Krammer representation of the group of conjugating automorphisms C₃
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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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