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

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2013-07-30 DOI:10.4171/QT/78

Alexander P. Ellis, Aaron D. Lauda

引用次数: 15

Abstract

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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$U_q (\mathfrak{sl}_2)$的奇分类

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)。

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.