Regular Kac-Moody superalgebras and integrable highest weight modules

TL;DR

This paper introduces regular Kac-Moody superalgebras, classifies them via integrable modules, and establishes conditions for the integrability of their highest weight modules, contributing to the classification of finite-growth contragredient Lie superalgebras.

Contribution

It defines and classifies regular Kac-Moody superalgebras and provides criteria for the integrability of their highest weight modules, advancing the understanding of Lie superalgebra classifications.

Findings

Classification of regular Kac-Moody superalgebras

Conditions for integrable highest weight modules

Progress towards classifying finite-growth contragredient Lie superalgebras

Abstract

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras.