Implicit structure in 2-representations of quantum groups

• Sabin Cautis ^[1] ; Aaron D. Lauda ^[2]
  1. [1] University of British Columbia

     University of British Columbia

     Canadá

     
  2. [2] University of Southern California

     University of Southern California

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 21, Nº. 1, 2015, págs. 201-244
• Idioma: inglés
• Enlaces
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• Resumen

  • 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.