Finite Linear Quotients of \B₃ of Low Dimension

2008/06/01 by Eric C. Rowell, Rowell, Eric C., Imre Tuba +1
Mathematics · #20F36 (Primary) 20C15 (Secondary) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0806.0168

openalex publication_date 2008/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of deciding whether or not the image of an irreducible representation of the braid group \B₃ of degree ≤ 5 has finite image if we are only given the eigenvalues of a generator. We provide a partial algorithm that determines when the images are finite or infinite in all but finitely many cases, and use these results to study examples coming from quantum groups. Our technique uses two classification theorems and the computational group theory package GAP.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups

Related

• Braid representations from quantum groups of exceptional Lie type
• Representations of the braid group B₃ and of SL(2,Z)
• A note on certain finite-dimensional representations of the braid group
• Finite image homomorphisms of the braid group and its generalizations
• Parametrization of representations of braid groups