Quantum Borcherds-Bozec algebras via semi-derived Ringel-Hall algebras II: braid group actions

Abstract

Based on the realization of quantum Borcherds-Bozec algebra $\tilde{\mathbf{U}}$ and quantum generalized Kac-Moody algebra ${}^B\tilde{\mathbf{U}}$ via semi-derived Ringel-Hall algebra of a quiver with loops, we deduce the braid group actions of $\tilde{\mathbf{U}}$ introduced by Fan and Tong recently and establish braid group actions for ${}^B\tilde{\mathbf{U}}$ by applying the BGP reflection functors to semi-derived Ringel-Hall algebras.

18 pages, minor changes, accepted by Bulletin of the London Mathematical Society. arXiv admin note: substantial text overlap with arXiv:2107.03160