Skein and cluster algebras with coefficients for unpunctured surfaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910572553961472 |
|---|---|
| author | Ishibashi, Tsukasa Kano, Shunsuke Yuasa, Wataru |
| author_facet | Ishibashi, Tsukasa Kano, Shunsuke Yuasa, Wataru |
| contents | We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra $\mathscr{S}_{Σ,\mathbb{W}}^{A}$ of a walled surface $(Σ,\mathbb{W})$, and prove that it has a quantum cluster structure. The walled surfaces naturally generalize the marked surfaces with multi-laminations, which have been used to describe the quantum cluster algebras of geometric type for marked surfaces by Fomin--Thurston [FT18]. Moreover, we give skein theoretic interpretation for some of quasi-homomorphisms [Fra16] between these quantum cluster algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02861 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Skein and cluster algebras with coefficients for unpunctured surfaces Ishibashi, Tsukasa Kano, Shunsuke Yuasa, Wataru Geometric Topology Quantum Algebra 13F60, 57K31 (Primary), 57K20 (Secondary) We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra $\mathscr{S}_{Σ,\mathbb{W}}^{A}$ of a walled surface $(Σ,\mathbb{W})$, and prove that it has a quantum cluster structure. The walled surfaces naturally generalize the marked surfaces with multi-laminations, which have been used to describe the quantum cluster algebras of geometric type for marked surfaces by Fomin--Thurston [FT18]. Moreover, we give skein theoretic interpretation for some of quasi-homomorphisms [Fra16] between these quantum cluster algebras. |
| title | Skein and cluster algebras with coefficients for unpunctured surfaces |
| topic | Geometric Topology Quantum Algebra 13F60, 57K31 (Primary), 57K20 (Secondary) |
| url | https://arxiv.org/abs/2312.02861 |