The knot invariant associated to two-parameter quantum algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916541828694016 |
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| author | Fan, Zhaobing Xing, Junjing |
| author_facet | Fan, Zhaobing Xing, Junjing |
| contents | Using the skew-Hopf pairing, we obtain $\mathcal{R}$-matrix for the two-parameter quantum algebra $U_{v,t}$. We further construct a strict monoidal functor $\mathcal{T}$ from the tangle category $(\mathrm{OTa},\otimes, \emptyset)$ to the category $(\mathrm{Mod},\otimes, \mathbb{Q}(v,t))$ of $U_{v,t}$-modules . As a consequence, the quantum knot invariant of the tangle $L$ of type $(n,n)$ is obtained by the action of $\mathcal{T}$ on the closure $\tilde{L}$ of $L$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_10478 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The knot invariant associated to two-parameter quantum algebras Fan, Zhaobing Xing, Junjing Quantum Algebra 17B37, 18M15, 57K14 Using the skew-Hopf pairing, we obtain $\mathcal{R}$-matrix for the two-parameter quantum algebra $U_{v,t}$. We further construct a strict monoidal functor $\mathcal{T}$ from the tangle category $(\mathrm{OTa},\otimes, \emptyset)$ to the category $(\mathrm{Mod},\otimes, \mathbb{Q}(v,t))$ of $U_{v,t}$-modules . As a consequence, the quantum knot invariant of the tangle $L$ of type $(n,n)$ is obtained by the action of $\mathcal{T}$ on the closure $\tilde{L}$ of $L$. |
| title | The knot invariant associated to two-parameter quantum algebras |
| topic | Quantum Algebra 17B37, 18M15, 57K14 |
| url | https://arxiv.org/abs/2203.10478 |