Exchange relation planar algebras of small rank
Exchange relation planar algebras of small rank
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DOI：
10.1090/tran/6582
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发表时间：
2013-08
影响因子：
1.3
通讯作者：
Zhengwei Liu
中科院分区：
文献类型：
--
作者：
Zhengwei Liu
本文的主要目的是对具有4维2-盒的交换关系平面代数进行分类。除了它的绞理论，我们强调的积极性的子因子平面代数的基础上Schur产品定理。我们将讨论2-盒的投影格，特别是投影的秩。从这一点出发，得到了关于双投影的几个结果。分类的关键突破是证明双投影的存在。利用这一方法，我们还对另外两类子因子平面代数进行了分类，一类是由2-盒生成的子因子平面代数，它具有4维2-盒和至多23维3-盒;另一类是由2-盒生成的子因子平面代数，使得3-盒与基本构造理想的商是交换的.它们推广了Bisch，Jones和作者所得到的单生成平面代数的分类.
The main purpose of this paper is to classify exchange relation planar algebras with 4 dimensional 2-boxes. Besides its skein theory, we emphasize the positivity of subfactor planar algebras based on the Schur product theorem. We will discuss the lattice of projections of 2-boxes, specifically the rank of the projections. From this point, several results about biprojections are obtained. The key break of the classification is to show the existence of a biprojection. By this method, we also classify another two families of subfactor planar algebras, subfactor planar algebras generated by 2-boxes with 4 dimensional 2-boxes and at most 23 dimensional 3-boxes; subfactor planar algebras generated by 2-boxes, such that the quotient of 3-boxes by the basic construction ideal is abelian. They extend the classification of singly generated planar algebras obtained by Bisch, Jones and the author.