Classification of Thurston relation subfactor planar algebras
Classification of Thurston relation subfactor planar algebras
复制标题
瑟斯顿关系子因子平面代数的分类
作者：
Corey Jones;Zhengwei Liu;Yunxiang Ren
Bisch和Jones提出了平面代数的Skein理论分类，并与第二作者一起研究了由2-盒生成的平面代数的Skein理论分类。本文考虑了3-盒生成元，并对满足瑟斯顿关系的非平凡3-盒生成的子因子平面代数进行了分类。分类中的子因子平面代数可以是$E^6，也可以是量子表示的子因子平面代数。我们介绍了一种判定平面代数正性的新方法和降低计算复杂度的新技巧。
Bisch and Jones suggested the skein theoretic classification of planar algebras and investigated the ones generated by 2-boxes with the second author. In this paper, we consider 3-box generators and classify subfactor planar algebras generated by a non-trivial 3-box satisfying a relation proposed by Thurston. The subfactor planar algebras in the classification are either $E^6$ or the ones from representations of quantum $SU(N)$. We introduce a new method to determine positivity of planar algebras and new techniques to reduce the complexity of computations.