NDLI: Monoidal Supercategories

Content Provider	Springer Nature Link
Author	Brundan, Jonathan Ellis, Alexander P.
Copyright Year	2017
Abstract	This work is a companion to our article “Super Kac–Moody 2-categories,” which introduces super analogs of the Kac–Moody 2-categories of Khovanov–Lauda and Rouquier. In the case of $${\mathfrak{sl}_2}$$ , the super Kac–Moody 2-category was constructed already in [A. Ellis and A. Lauda, “An odd categorification of $${U_q(\mathfrak{sl}_2)}$$ ”], but we found that the formalism adopted there became too cumbersome in the general case. Instead, it is better to work with 2-supercategories (roughly, 2-categories enriched in vector superspaces). Then the Ellis–Lauda 2-category, which we call here a $${\Pi}$$ -2-category (roughly, a 2-category equipped with a distinguished involution in its Drinfeld center), can be recovered by taking the superadditive envelope then passing to the underlying 2-category. The main goal of this article is to develop this language and the related formal constructions in the hope that these foundations may prove useful in other contexts.
Starting Page	1045
Ending Page	1089
Page Count	45
File Format	PDF
ISSN	00103616
Journal	Communications in Mathematical Physics
Volume Number	351
Issue Number	3
e-ISSN	14320916
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2017-03-07
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Mathematical Physics Quantum Physics Complex Systems Classical and Quantum Gravitation, Relativity Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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