Cyclicity for categorified quantum groups

TL;DR

This paper introduces a cyclic duality functor for the categorified quantum group associated with KLR algebras, using a modified diagrammatic approach to enhance the structure's symmetry and coherence.

Contribution

It provides a novel cyclic duality construction for categorified quantum groups, extending the diagrammatic formalism to achieve this property.

Findings

Established a cyclic duality functor for categorified quantum groups

Modified the diagrammatic formalism to incorporate cyclicity

Enhanced the structural symmetry of 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.