Regular subalgebras of affine Kac-Moody algebras

TL;DR

This paper classifies regular subalgebras of affine Kac-Moody algebras by their root systems, revealing that such root systems are intersections with sublattices, and explores applications to hyperbolic and conformally invariant subalgebras.

Contribution

It provides a complete classification of regular subalgebras of affine Kac-Moody algebras based on their root systems, linking them to sublattices.

Findings

Root system of a subalgebra is an intersection with a sublattice

Classification of regular subalgebras based on root systems

Applications to hyperbolic and conformally invariant subalgebras

Abstract

We classify regular subalgebras of affine Kac-Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersection of the root system of the algebra with a sublattice of its root lattice. We also discuss applications to investigations of regular subalgebras of hyperbolic Kac-Moody algebras and conformally invariant subalgebras of affine Kac-Moody algebras.