Resumen de Implicit structure in 2-representations of quantum groups

Sabin Cautis, Aaron D. Lauda

• 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.