Braiding Operator via Quantum Cluster Algebra
Quantum Algebra
2014-11-19 v3 Mathematical Physics
Geometric Topology
math.MP
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.
Cite
@article{arxiv.1404.2009,
title = {Braiding Operator via Quantum Cluster Algebra},
author = {Kazuhiro Hikami and Rei Inoue},
journal= {arXiv preprint arXiv:1404.2009},
year = {2014}
}
Comments
20 pages