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arxiv: 1111.1431 · v3 · pith:OKZORS2Snew · submitted 2011-11-06 · 🧮 math.QA · math.RT

Implicit structure in 2-representations of quantum groups

Sabin Cautis , Aaron D. Lauda This is my paper
classification 🧮 math.QA math.RT
keywords definitiongroupsimplicitkhovanov-laudaquantumrepresentationrouquiersense
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Given a strong 2-representation of a Kac-Moody Lie algebra (in the sense of Rouquier) we show how to extend it to a 2-representation of categorified quantum groups (in the sense of Khovanov-Lauda). This involves checking certain extra 2-relations which are explicit in the definition by Khovanov-Lauda and, as it turns out, implicit in Rouquier's definition. Some applications are also discussed.

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  1. Action of the Witt algebra on categorified quantum groups

    math.QA 2025-07 unverdicted novelty 6.0

    Constructs an action of the positive Witt algebra on categorified quantum groups for simply-laced Lie algebras, recovering the foam action in type A and inducing the current-algebra action via trace decategorification.