Keywords
Braid group, Free group, Lawrence-Krammer-Bigelow representation, Burau representation, faithfulness
Disciplines
Other Applied Mathematics
Abstract
Let $C_n$ be the group of conjugating automorphisms. V. Bardakov defined a representation $\rho$ of $C_n$, which is an extension of Lawrence-Krammer-Bigelow representation of the braid group $B_n$. Bardakov proved that the representation $\rho$ is unfaithful for $n \geq 5$. The cases $n=3,4$ remain open. M. N. Nasser and M. N. Abdulrahim made attempts towards the faithfulness of $\rho$ in the case $n=3$. In this work, we prove that $\rho$ is unfaithful in the both cases $n=3$ and $n=4$.
Author ORCID Identifier
Mohamad Nasser - https://orcid.org/0009-0005-0673-0113
Recommended Citation
Nasser, Mohamad
(2024)
"THE FAITHFULNESS OF AN EXTENSION OF LAWRENCE-KRAMMER-BIGELOW REPRESENTATION ON THE GROUP OF CONJUGATING AUTOMORPHISMS $C_n$ in the cases $n=3$ and $n=4$,"
BAU Journal - Science and Technology: Vol. 6:
Iss.
1, Article 1.
DOI: https://doi.org/10.54729/2959-331X.1151
ISSN
2959-331X