Thurston关系子因子平面代数的分类

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2016-06-02 DOI:10.4171/qt/126

Corey Jones, Zhengwei Liu, Yunxiang Ren

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引用次数: 4

摘要

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。

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Classification of Thurston relation subfactor planar algebras

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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