Quantum Borcherds-Bozec Superalgebras

TL;DR

This paper introduces quantum Borcherds-Bozec superalgebras, establishing foundational results such as bilinear forms, Serre relations, and character formulas, and proves the semi-simplicity of their integrable representations.

Contribution

It presents the definition and fundamental properties of quantum Borcherds-Bozec superalgebras, including key structural and representation-theoretic results.

Findings

Established a bilinear form for the superalgebras

Proved higher Serre relations and quasi-R-matrix existence

Derived character formulas and proved semi-simplicity of integrable modules

Abstract

We introduce quantum Borcherds-Bozec superalgebras. We present and prove various results of the quantum superalgebras including a bilinear form, higher Serre relation, quasi-R-matrix, character formula for the irreducible highest weight modules. We also prove the category of integrable representations is semi-simple.