Quantum groups of Borcherds-Cartan type and Khovanov-Lauda-Rouquier algebras

2024/12/30 by Kang, Stefano V., Kim, Young Rock, Tong, Bolun
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2501.06209

Abstract

We study a class of quantum groups U^- associated with quivers with loops and provide a categorification by constructing their associated Khovanov-Lauda-Rouquier algebras R. We prove that the indecomposable projective module over R corresponds to the canonical basis of U^-. In the Jordan quiver case, we show that the cyclotomic Khovanov-Lauda-Rouquier algebras R^Λ categorify the irreducible highest weight U-module V(Λ).

Related

• Categorification of quantum Borcherds-Bozec algebras
• Hall categories and KLR categorification
• Quantum Borcherds-Bozec algebras via semi-derived Ringel-Hall algebras
• Quiver Hecke algebras for Borcherds-Cartan datum II
• Quantum Algebras and Cyclic Quiver Varieties