Hamiltonian Extended Affine Lie Algebras and its representation theory

TL;DR

This paper introduces Hamiltonian Extended Lie Algebras (HEALAs), a new class of extended affine Lie algebras, and classifies their irreducible integrable modules based on Hamiltonian algebra modules.

Contribution

It defines HEALAs, connects their derivation algebra to Hamiltonian algebra, and classifies their irreducible modules, advancing the understanding of their representation theory.

Findings

Classification of irreducible integrable modules for HEALAs

Connection between HEALAs and Hamiltonian algebra modules

Extension of representation theory for affine Lie algebras

Abstract

We introduce a new class of extended affine Lie algebras called Hamiltonian Extended Lie Algebras(HEALAs). They are so called because the corresponding derivation algebra is the classical Hamiltonian algebra. We classify the irreducible integrable modules for the HEALA based on the classification of irreducible Jet modules for the Hamiltonian algebra (both zero level and non-zero level.