Braiding operator via quantum cluster algebra

Kazuhiro Hikami, Rei Inoue

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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

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All Science Journal Classification (ASJC) codes

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

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