A note on double affine Hecke algebra for skein algebra on twice-punctured torus

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-12-20 DOI:10.1016/j.geomphys.2024.105408

Kazuhiro Hikami

引用次数: 0

Abstract

We construct a generalization of the

C^{\lor} C_{1}

-type double affine Hecke algebra for the skein algebra on the twice-punctured torus

Σ_{1, 2}

using the Heegaard dual of the Iwahori–Hecke operator recently introduced in our previous article. We show that the automorphisms of our algebra correspond to the Dehn twists about the curves on

Σ_{1, 2}

. We also give the cluster algebraic construction of the classical limit of the skein algebra, where the Dehn twists are given in terms of the cluster mutations.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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