Hyperbolic Kac-Moody superalgebras

TL;DR

This paper classifies hyperbolic Kac-Moody superalgebras, detailing their finite types, ranks, diagrams, root systems, and introduces a folding method for sub(super)algebras.

Contribution

It provides the first comprehensive classification of hyperbolic Kac-Moody superalgebras, including their diagrams and root systems, and explores folding procedures for sub(super)algebras.

Findings

213 hyperbolic Kac-Moody superalgebras identified

Dynkin-Kac diagrams and root systems determined

Folding procedure for sub(super)algebras discussed

Abstract

We present a classification of the hyperbolic Kac-Moody (HKM) superalgebras. The HKM superalgebras of rank larger or equal than 3 are finite in number (213) and limited in rank (6). The Dynkin-Kac diagrams and the corresponding simple root systems are determined. We also discuss a class of singular sub(super)algebras obtained by a folding procedure.