Presentations of Kauffman bracket skein algebras of planar surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909058997420032 |
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| author | Chen, Haimiao |
| author_facet | Chen, Haimiao |
| contents | Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $Σ_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by explicit generators and relations. The presentation is independent of $R$, and can be considered as a quantization of the trace algebra of $n$ generic $2\times 2$ unimodular matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00898 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Presentations of Kauffman bracket skein algebras of planar surfaces Chen, Haimiao Geometric Topology Quantum Algebra 57K16, 57K31 Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $Σ_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by explicit generators and relations. The presentation is independent of $R$, and can be considered as a quantization of the trace algebra of $n$ generic $2\times 2$ unimodular matrices. |
| title | Presentations of Kauffman bracket skein algebras of planar surfaces |
| topic | Geometric Topology Quantum Algebra 57K16, 57K31 |
| url | https://arxiv.org/abs/2401.00898 |