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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2309.01011 |
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| _version_ | 1866916435650936832 |
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| author | Arthamonov, S. |
| author_facet | Arthamonov, S. |
| contents | We show that one-parameter deformation $\mathcal A_{q,t}$ of the skein algebra $Sk_q(Σ_2)$ of a genus two surface suggested in [AS19] is flat. We solve the word problem in the algebra and describe monomial basis. In addition, we calculate the classical limit $\mathcal A_{q=1,t}$ of the algebra and prove that it is a one-parameter flat Poisson deformation of the coordinate ring $\mathcal A_{q=t=1}$ of an $SL(2,\mathbb C)$-charater variety of a genus two surface. As a byproduct, we obtain a remarkably simple presentation in terms of generators and relations for the coordinate ring $\mathcal A_{q=t=1}$ of a genus two character variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01011 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classical Limit of genus two DAHA Arthamonov, S. Quantum Algebra Mathematical Physics Rings and Algebras 17B37, 20G42, 81R50, 37J39 We show that one-parameter deformation $\mathcal A_{q,t}$ of the skein algebra $Sk_q(Σ_2)$ of a genus two surface suggested in [AS19] is flat. We solve the word problem in the algebra and describe monomial basis. In addition, we calculate the classical limit $\mathcal A_{q=1,t}$ of the algebra and prove that it is a one-parameter flat Poisson deformation of the coordinate ring $\mathcal A_{q=t=1}$ of an $SL(2,\mathbb C)$-charater variety of a genus two surface. As a byproduct, we obtain a remarkably simple presentation in terms of generators and relations for the coordinate ring $\mathcal A_{q=t=1}$ of a genus two character variety. |
| title | Classical Limit of genus two DAHA |
| topic | Quantum Algebra Mathematical Physics Rings and Algebras 17B37, 20G42, 81R50, 37J39 |
| url | https://arxiv.org/abs/2309.01011 |