Quantum Borcherds-Bozec algebras and their integrable representations

TL;DR

This paper explores quantum Borcherds-Bozec algebras, establishing their structural properties and the semi-simplicity of their integrable representations, contributing to the understanding of their algebraic and representation-theoretic features.

Contribution

It proves the triangular decomposition of quantum Borcherds-Bozec algebras and shows the category of their integrable representations is semi-simple, advancing the theoretical framework.

Findings

Quantum Borcherds-Bozec algebras have a triangular decomposition.

The category of integrable representations is semi-simple.

The paper establishes fundamental properties of these algebras.

Abstract

We investigate the fundamental properties of quantum Borcherds-Bozec algebras and their representations. Among others, we prove that the quantum Borcherds-Bozec algebras have a triangular decomposition and the category of integrable representations is semi-simple.