Center of stated $\mathrm{SL}(n)$-skein algebras: even roots of unity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908555533090816 |
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| author | Karuo, Hiroaki Wang, Zhihao |
| author_facet | Karuo, Hiroaki Wang, Zhihao |
| contents | We describe the center of quantum tori appearing in quantum higher Teichmüller theory when the quantum parameter is an even root of unity. This is a subsequent of the work in the odd roots of unity case. The centers of the quantum tori help to understand those of (reduced) stated $\mathrm{SL}(n)$-skein algebras via quantum trace maps. Moreover, we compute the PI-degree of the quantum tori, which are the same with those of (reduced) stated $\mathrm{SL}(n)$-skein algebras. As corollaries, we give matrix decompositions for anti-symmetric integer matrices for the quantum tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18950 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Center of stated $\mathrm{SL}(n)$-skein algebras: even roots of unity Karuo, Hiroaki Wang, Zhihao Geometric Topology Quantum Algebra Representation Theory We describe the center of quantum tori appearing in quantum higher Teichmüller theory when the quantum parameter is an even root of unity. This is a subsequent of the work in the odd roots of unity case. The centers of the quantum tori help to understand those of (reduced) stated $\mathrm{SL}(n)$-skein algebras via quantum trace maps. Moreover, we compute the PI-degree of the quantum tori, which are the same with those of (reduced) stated $\mathrm{SL}(n)$-skein algebras. As corollaries, we give matrix decompositions for anti-symmetric integer matrices for the quantum tori. |
| title | Center of stated $\mathrm{SL}(n)$-skein algebras: even roots of unity |
| topic | Geometric Topology Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2509.18950 |