论文标题
较高排名的Askey-Wilson代数为绞线代数
Higher Rank Askey-Wilson Algebras as Skein Algebras
论文作者
论文摘要
在本文中，我们通过证明$（n+1）$刺破的球体的律师括号（n+1）$（n-2）$（n-2）$ ASKEY-WILSON代数给出了拓扑解释和图形计算。为此，我们考虑了$ n $副本的Askey-Wilson代数$ n $副本$ \ mathcal {u} _Q {（\ Mathfrak {\ Mathfrak {sl} _2 _2）} $或reflection eargee eargebra。然后，我们使用$（n+1）$ - 刺穿的球体的Kauffman支架skein代数的异构主义，并使用$ \ mathcal {u} _q {（\ slfrak {\ mathfrak {sl} _2} _2} _2}）$ novariants $ novariants $ novariants $ novariants $ novariants。我们还找到了$ \ Mathcal {u} _Q {（\ Mathfrak {\ Mathfrak {sl} _2}）$不变式的分级矢量空间维度，并将其应用于五个功能的Skein代数的介绍，并在五个功能的Skein代数中找到了这一点。
In this paper we give a topological interpretation and diagrammatic calculus for the rank $(n-2)$ Askey-Wilson algebra by proving there is an explicit isomorphism with the Kauffman bracket skein algebra of the $(n+1)$-punctured sphere. To do this we consider the Askey-Wilson algebra in the braided tensor product of $n$ copies of either the quantum group $\mathcal{U}_q{(\mathfrak{sl}_2)}$ or the reflection equation algebra. We then use the isomorpism of the Kauffman bracket skein algebra of the $(n+1)$-punctured sphere with the $\mathcal{U}_q{(\mathfrak{sl}_2})$ invariants of the Aleeksev moduli algebra to complete the correspondence. We also find the graded vector space dimension of the $\mathcal{U}_q{(\mathfrak{sl}_2})$ invariants of the Aleeksev moduli algebra and apply this to finding a presentation of the skein algebra of the five-punctured sphere and hence also find a presentation for the rank $2$ Askey-Wilson algebra.
