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

TL;DR

This paper constructs and analyzes braid group actions on quantum Borcherds-Bozec and generalized Kac-Moody algebras using semi-derived Ringel-Hall algebras and BGP reflection functors, extending previous work.

Contribution

It introduces new braid group actions for quantum Borcherds-Bozec and generalized Kac-Moody algebras via semi-derived Ringel-Hall algebra techniques.

Findings

Established braid group actions for quantum Borcherds-Bozec algebra.

Extended braid group actions to quantum generalized Kac-Moody algebra.

Connected algebraic structures with BGP reflection functors.

Abstract

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