论文标题
泊松和绞线代数与循环相关的代数
Center of Poisson and skein algebras associated to loops on surfaces
论文作者
论文摘要
我们讨论并开发了一种系统的方法，以计算与Goldman和Wolpert在80年代引入的可定向表面（可能是边界和穿刺）上循环的各种泊松代数相关的泊松中心（Casimir），同时研究了瑟斯顿地震的变形。我们的计算扩展了ETINGOF的结果到所有有限型双曲线表面。我们使用这些方法来计算Turaev引入的各种代数量代数的中心，以量化这些泊松代数。作为我们结果的另一个应用，我们计算了Hoste和Przytycki引入的同型绞线代数的中心。
We discuss and develop a systematic method to compute the Poisson center (Casimir) of various Poisson algebras associated to loops on orientable surfaces (possibly with boundary and punctures) introduced by Goldman and Wolpert in 80's while studying Thurston's earthquakes deformations. Our computation extends a result of Etingof to all finite type hyperbolic surfaces. We use these methods to compute the center of various skein algebras introduced by Turaev for the quantization of these Poisson algebras. As another application of our results we compute the center of homotopy skein algebra introduced by Hoste and Przytycki.
