pith. sign in

arxiv: 1404.2009 · v3 · pith:42M23TD2new · submitted 2014-04-08 · 🧮 math.QA · math-ph· math.GT· math.MP

Braiding Operator via Quantum Cluster Algebra

Kazuhiro Hikami , Rei Inoue This is my paper
classification 🧮 math.QA math-phmath.GTmath.MP
keywords braidingoperatorquantumalgebraclusterassignedconstructdilogarithm
0
0 comments X
read the original abstract

We construct a braiding operator in terms of the quantum dilogarithm function based on the quantum cluster algebra. We show that it is a q-deformation of the R-operator for which hyperbolic octrahedron is assigned. Also shown is that, by taking q to be a root of unity, our braiding operator reduces to the Kashaev R-matrix up to a simple gauge-transformation.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms

    math.QA 2025-09 unverdicted novelty 5.0

    Derives explicit factorization of the holonomy R-matrix for U_ξ(sl₂) at a root of unity into four geometric quantum dilogarithms satisfying a holonomy Yang-Baxter equation.