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

Abstract

We categorify a class of quantum groups associated with quivers, possibly with loops, by constructing the corresponding Khovanov-Lauda-Rouquier algebras (KLR) algebras $R$. We prove that the indecomposable projective $R$-modules realize the canonical basis of the negative part $U^{-}$ of the quantum group. Moreover, for $\Lambda \in P^{+}$, the cyclotomic KLR algebra $R^{\Lambda }$ provide a categorification of the irreducible highest weight $U$-module $V(\Lambda )$.

arXiv admin note: substantial text overlap with arXiv:2406.18378