REWRITING MODULO ISOTOPIES IN KHOVANOV-LAUDA-ROUQUIER'S CATEGORIFICATION OF QUANTUM GROUPS

Benjamin Dupont (1)

1 AGL - Algèbre, géométrie, logique

We study a presentation of Khovanov-Lauda-Rouquier's candidate 2-categorification of a quantum group using algebraic rewriting methods. We use a computational approach based on rewriting modulo the isotopy axioms of its pivotal structure to compute a family of linear bases for all the vector spaces of 2-cells in this 2-category. We show that these bases correspond to Khovanov and Lauda's conjectured generating sets, proving the non-degeneracy of their diagrammatic calculus. This implies that this 2-category is a categorification of Lusztig's idempotent and integral quantum group U q (g) associated to a symmetrizable simply-laced Kac-Moody algebra g.

Mots clés: Rewriting modulo; Linear polygraphs; Higher-dimensional linear categories; KLR algebras; Quantum groups

Domaines: Théorie des représentations [math.RT]; Catégories et ensembles [math.CT]; Algèbres quantiques [math.QA]

Benjamin Dupont. REWRITING MODULO ISOTOPIES IN KHOVANOV-LAUDA-ROUQUIER'S CATEGORIFICATION OF QUANTUM GROUPS. 2019. ⟨hal-02263267⟩