Classification of Thurston relation subfactor planar algebras

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2016-06-02 DOI:10.4171/qt/126

Corey Jones, Zhengwei Liu, Yunxiang Ren

引用次数: 4

Abstract

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.

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Thurston关系子因子平面代数的分类

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-box生成的平面代数。本文考虑3-盒生成器，并对满足Thurston提出的关系的非平凡3-盒生成的子因子平面代数进行分类。分类中的子因子平面代数为$E^6$或来自量子$SU(N)$表示的子因子平面代数。介绍了一种确定平面代数正性的新方法和降低计算复杂度的新技术。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.