### 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 R^{K}-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 language | English |
---|---|

Article number | 474006 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 47 |

DOIs | |

Publication status | Published - 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)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*47*(47), [474006]. https://doi.org/10.1088/1751-8113/47/47/474006

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 47, no. 47, 474006. https://doi.org/10.1088/1751-8113/47/47/474006

}

TY - JOUR

T1 - Braiding operator via quantum cluster algebra

AU - Hikami, Kazuhiro

AU - Inoue, Rei

PY - 2014/11/28

Y1 - 2014/11/28

N2 - 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'.

AB - 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'.

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UR - http://www.scopus.com/inward/citedby.url?scp=84910615536&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/47/47/474006

DO - 10.1088/1751-8113/47/47/474006

M3 - Article

AN - SCOPUS:84910615536

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 47

M1 - 474006

ER -