Cyclicity for categorified quantum groups

Abstract

We equip the categorified quantum group attached to a KLR algebra and an arbitrary choice of scalars with duality functor which is cyclic, that is, such that f=f^** for all 2-morphisms f. This is accomplished via a modified diagrammatic formalism.

12 pages, xy-pic diagrams

References in corpus (7)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• On the center of quiver-Hecke algebras
• The ${\mathfrak{sl}}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• Current algebras and categorified quantum groups
• Centers of KLR algebras and cohomology rings of quiver varieties
• On the definition of Kac-Moody 2-category

Cited by in corpus (12)

• Categorification of quantum symmetric pairs I
• Current algebras and categorified quantum groups
• Lecture notes on 2-dimensional defect TQFT
• Annular Evaluation and Link Homology
• Heisenberg and Kac-Moody categorification
• Super Kac-Moody 2-categories
• Centers of KLR algebras and cohomology rings of quiver varieties
• Braid group actions from categorical symmetric Howe duality on deformed Webster algebras
• Parameters in categorified quantum groups
• Curved Rickard complexes and link homologies
• Categorification of the internal braid group action for quantum groups I: 2-functoriality
• Trace and categorical sl(n) representations