On the Faithfulness of the Extension of Lawrence-Krammer Representation of the Group of Conjugating Automorphisms C3
Authors
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Department of Mathematics and Computer Science, Beirut Arab University, P.O. Box 11-5020, Beirut ,LB
Mohamad N. Nasser -
Department of Mathematics and Computer Science, Beirut Arab University, P.O. Box 11-5020, Beirut ,LBMohammad N. Abdulrahim
DOI:
https://doi.org/10.18311/jims/2023/29869Keywords:
Braid Group, Free Group, Lawrence–Krammer Representation, Burau Representation, Faithfulness.Abstract
Let Cn be the group of conjugating automorphisms. We study the representation ρ of Cn, an extension of Lawrence-Krammer representation of the braid group Bn. It is known that the representation ρ is unfaithful for n ≥ 5, the cases n = 3, 4 remain open. In our work, we make attempts towards the faithfulness of ρ in the case n = 3.
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Copyright (c) 2023 Mohamad N. Nasser, Mohammad N. Abdulrahim
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2022-03-29
Published 2023-07-12
References
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