论文标题
表面上的绞线代数和集群代数的兼容性的后果
Consequences of the compatibility of skein algebra and cluster algebra on surfaces
论文作者
论文摘要
我们研究了带有穿刺的拓扑表面上的两个曲线代数 - Fomin，Shapiro和Thurston定义的表面群集代数，以及由Roger和Yang构建的广义的Skein代数。通过建立它们的兼容性，我们解决了Roger-Yang对装饰的Teichmuller空间的变形量化的猜想。我们还可以在表面群集代数上获得几个结构性结果。正属表面的群集代数没有有限生成，并且与其上簇代数不同。
We investigate two algebra of curves on a topological surface with punctures - the cluster algebra of surfaces defined by Fomin, Shapiro, and Thurston, and the generalized skein algebra constructed by Roger and Yang. By establishing their compatibility, we resolve Roger-Yang's conjecture on the deformation quantization of the decorated Teichmuller space. We also obtain several structural results on the cluster algebra of surfaces. The cluster algebra of a positive genus surface is not finitely generated, and it differs from its upper cluster algebra.
