$U_q (\mathfrak{sl}_2)$的奇分类

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2013-07-30 DOI:10.4171/QT/78

Alexander P. Ellis, Aaron D. Lauda

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引用次数: 15

摘要

我们定义了一个对Clark和Wang引入的sl(2)的覆盖Kac-Moody代数进行分类的2范畴。这种分类形成了由Kang、Kashiwara和Oh提出的超2类结构。超2类结构引入了一个(Z x Z_2)分级，使其Grothendieck群在Z x Z_2的群代数上具有自由模的结构。通过将Z_2-action专门化到+1或-1，该构造分别专门化到一个“奇数”分类sl(2)和一个超分类osp(1 bb0 2)。

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An odd categorification of $U_q (\mathfrak{sl}_2)$

We define a 2-category that categorifies the covering Kac-Moody algebra for sl(2) introduced by Clark and Wang. This categorification forms the structure of a super-2-category as formulated by Kang, Kashiwara, and Oh. The super-2-category structure introduces a (Z x Z_2)-grading giving its Grothendieck group the structure of a free module over the group algebra of Z x Z_2. By specializing the Z_2-action to +1 or to -1, the construction specializes to an "odd" categorification of sl(2) and to a supercategorification of osp(1|2), respectively.

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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.