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

Benjamin Dupont 1
1 AGL - Algèbre, géométrie, logique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : 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.
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Submitted on : Saturday, August 3, 2019 - 4:51:43 PM
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Benjamin Dupont. REWRITING MODULO ISOTOPIES IN KHOVANOV-LAUDA-ROUQUIER'S CATEGORIFICATION OF QUANTUM GROUPS. 2019. ⟨hal-02263267⟩

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