### 抄録

We use Bonahon-Wong’s trace map to study character varieties of the oncepunctured torus and of the 4-punctured sphere. We clarify a relationship with cluster algebra associated with ideal triangulations of surfaces, and we show that the Goldman Poisson algebra of loops on surfaces is recovered from the Poisson structure of cluster algebra. It is also shown that cluster mutations give the automorphism of the character varieties. Motivated by a work of Chekhov-Mazzocco-Rubtsov, we revisit con uences of punctures on sphere from cluster algebraic viewpoint, and we obtain associated affine cubic surfaces constructed by van der Put-Saito based on the Riemann-Hilbert correspondence. Further studied are quantizations of character varieties by use of quantum cluster algebra.

元の言語 | 英語 |
---|---|

記事番号 | 3 |

ジャーナル | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

巻 | 15 |

DOI | |

出版物ステータス | 出版済み - 1 1 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematical Physics
- Geometry and Topology

### これを引用

**Note on character varieties and cluster algebras.** / Hikami, Kazuhiro.

研究成果: ジャーナルへの寄稿 › 記事

}

TY - JOUR

T1 - Note on character varieties and cluster algebras

AU - Hikami, Kazuhiro

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We use Bonahon-Wong’s trace map to study character varieties of the oncepunctured torus and of the 4-punctured sphere. We clarify a relationship with cluster algebra associated with ideal triangulations of surfaces, and we show that the Goldman Poisson algebra of loops on surfaces is recovered from the Poisson structure of cluster algebra. It is also shown that cluster mutations give the automorphism of the character varieties. Motivated by a work of Chekhov-Mazzocco-Rubtsov, we revisit con uences of punctures on sphere from cluster algebraic viewpoint, and we obtain associated affine cubic surfaces constructed by van der Put-Saito based on the Riemann-Hilbert correspondence. Further studied are quantizations of character varieties by use of quantum cluster algebra.

AB - We use Bonahon-Wong’s trace map to study character varieties of the oncepunctured torus and of the 4-punctured sphere. We clarify a relationship with cluster algebra associated with ideal triangulations of surfaces, and we show that the Goldman Poisson algebra of loops on surfaces is recovered from the Poisson structure of cluster algebra. It is also shown that cluster mutations give the automorphism of the character varieties. Motivated by a work of Chekhov-Mazzocco-Rubtsov, we revisit con uences of punctures on sphere from cluster algebraic viewpoint, and we obtain associated affine cubic surfaces constructed by van der Put-Saito based on the Riemann-Hilbert correspondence. Further studied are quantizations of character varieties by use of quantum cluster algebra.

UR - http://www.scopus.com/inward/record.url?scp=85068124552&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068124552&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2019.003

DO - 10.3842/SIGMA.2019.003

M3 - Article

AN - SCOPUS:85068124552

VL - 15

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 3

ER -