A Proof of the Pentagon Relation for Skeins
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917105665835008 |
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| author | Hu, Mingyuan |
| author_facet | Hu, Mingyuan |
| contents | In \cite{HSZ23}, with Gus Schrader and Eric Zaslow we developed a skein-theoretic version of cluster theory, and made a conjecture on the pentagon relation for the skein dilogarithm. Here we give a topological proof of this conjecture. Combining \cite{MS21} and \cite{BCMN23}, we get a surjection from the skein algebra $\mathrm{Sk}^+(T - D)$ to the positive part of the elliptic Hall algebra $\mathcal{E}_{q, t}^+$. Hence our pentagon relation generalizes the ones in \cite{Z23} and \cite{GM19}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Proof of the Pentagon Relation for Skeins Hu, Mingyuan Quantum Algebra Mathematical Physics Geometric Topology Representation Theory In \cite{HSZ23}, with Gus Schrader and Eric Zaslow we developed a skein-theoretic version of cluster theory, and made a conjecture on the pentagon relation for the skein dilogarithm. Here we give a topological proof of this conjecture. Combining \cite{MS21} and \cite{BCMN23}, we get a surjection from the skein algebra $\mathrm{Sk}^+(T - D)$ to the positive part of the elliptic Hall algebra $\mathcal{E}_{q, t}^+$. Hence our pentagon relation generalizes the ones in \cite{Z23} and \cite{GM19}. |
| title | A Proof of the Pentagon Relation for Skeins |
| topic | Quantum Algebra Mathematical Physics Geometric Topology Representation Theory |
| url | https://arxiv.org/abs/2401.10817 |