What question did this study set out to answer?

The research aims to realize all irreducible integrable modules for extended affine Lie algebras of type A using quantum tori.

March 29, 2026Open Access

Integrable Representations for Extended Affine Lie Algebras Coordinated by Quantum Tori

Key Points

The research aims to realize all irreducible integrable modules for extended affine Lie algebras of type A using quantum tori.
Examined irreducible integrable modules for the core of the algebras.
Analyzed the action of center elements on these modules.
Investigated sufficient and necessary conditions for unitarity.
All irreducible integrable modules were effectively realized.
Conditions necessary for modules to be unitary were clearly outlined.

Abstract

In this paper we realize all irreducible integrable modules for the core of extended affine Lie algebras of type A coordinated by quantum tori with center elements act non-trivially.We also study the sufficient and necessary conditions for such modules to be unitary.

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