Integrable modules for Lie Torus

TL;DR

This paper classifies irreducible integrable modules for the universal central extension of centerless Lie Tori, revealing they are highest weight modules for sums of affine Lie algebras, advancing understanding of Extended Affine Lie algebras.

Contribution

It provides a classification of irreducible integrable modules for the universal central extension of centerless Lie Tori, connecting them to affine Lie algebra modules.

Findings

Irreducible integrable modules are highest weight modules.

Modules correspond to direct sums of affine Lie algebra modules.

Enhances understanding of the structure of Extended Affine Lie algebras.

Abstract

In the last two decades the structure of Extended Affine Lie algebras (EALA) is extensively studied. In explicitly constructing an EALA, the centerless Lie Torus play an important role. In this paper we consider the Universal central extension of a centerless Lie Torus and classify the irreducible integrable modules for them when the center acts non-trivially. They turn out to be "highest weight modules" for direct sum of finitely many affine Lie algebras.