Braiding Operator via Quantum Cluster Algebra

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.

20 pages

References in corpus (3)

• The quantum dilogarithm and representations quantum cluster varieties
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• On SL(2, C) quantum 6j-symbol and its relation to the hyperbolic volume