Band Bases as Common Triangular Bases in Cluster Algebras from Surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913179702919168 |
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| author | Qin, Fan Shen, Chao |
| author_facet | Qin, Fan Shen, Chao |
| contents | We consider the skein algebra of an unpunctured marked surface. Thurston previously constructed its band basis topologically. We show that this band basis coincides with the common triangular basis, which is a Kazhdan-Lusztig type basis for quantum cluster algebras analogous to the dual canonical basis of quantum groups. Our result confirms a conjecture of Thurston. It also provides new cases for the existence of the common triangular basis. In addition, we discover a phenomenon where certain unknots are arranged in configurations resembling beads on a necklace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Band Bases as Common Triangular Bases in Cluster Algebras from Surfaces Qin, Fan Shen, Chao Quantum Algebra Combinatorics Geometric Topology Rings and Algebras Representation Theory 13F60, 57M99, 05E99 We consider the skein algebra of an unpunctured marked surface. Thurston previously constructed its band basis topologically. We show that this band basis coincides with the common triangular basis, which is a Kazhdan-Lusztig type basis for quantum cluster algebras analogous to the dual canonical basis of quantum groups. Our result confirms a conjecture of Thurston. It also provides new cases for the existence of the common triangular basis. In addition, we discover a phenomenon where certain unknots are arranged in configurations resembling beads on a necklace. |
| title | Band Bases as Common Triangular Bases in Cluster Algebras from Surfaces |
| topic | Quantum Algebra Combinatorics Geometric Topology Rings and Algebras Representation Theory 13F60, 57M99, 05E99 |
| url | https://arxiv.org/abs/2606.02164 |