Note on character varieties and cluster algebras

研究成果: ジャーナルへの寄稿記事

1 引用 (Scopus)

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)
15
DOI
出版物ステータス出版済み - 1 1 2019

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Character Variety
Cluster Algebra
Cubic Surface
Poisson Algebra
Quantum Algebra
Poisson Structure
Automorphism
Triangulation
Hilbert
Quantization
Torus
Mutation
Correspondence
Trace

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

これを引用

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