Braiding operator via quantum cluster algebra

Kazuhiro Hikami, Rei Inoue

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 octahedron is assigned. Also shown is that, by taking q to be a root of unity, our braiding operator reduces to the Kashaev RK-matrix up to a simple gauge-transformation. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Cluster algebras in mathematical physics'.

Original languageEnglish
Article number474006
JournalJournal of Physics A: Mathematical and Theoretical
Volume47
Issue number47
DOIs
Publication statusPublished - Nov 28 2014

Fingerprint

Cluster Algebra
Quantum Algebra
Algebra
Mathematical operators
algebra
Physics
operators
Operator
Dilogarithm
Gages
Octahedron
Q-deformation
physics
Gauge Transformation
Roots of Unity
unity
matrices

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Braiding operator via quantum cluster algebra. / Hikami, Kazuhiro; Inoue, Rei.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 47, No. 47, 474006, 28.11.2014.

Research output: Contribution to journalArticle

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