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

2021/09/28 by Mohamad N. Nasser, Nasser, Mohamad N., Mohammad N. Abdulrahim +1
Mathematics · #20F36 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2109.13501

openalex publication_date 2021/09/28 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

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 ≥ 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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