Category $\mathcal{J}$ Modules for Hamiltonian Vector Fields on a Torus

TL;DR

This paper classifies the indecomposable and irreducible modules within category $al J$ for Hamiltonian vector fields on a torus, advancing understanding of their algebraic structure.

Contribution

It provides a classification of indecomposable and irreducible modules in category $al J$, a new result in the representation theory of Hamiltonian vector fields.

Findings

Classification of indecomposable modules

Classification of irreducible modules

Enhanced understanding of algebraic structures

Abstract

Modules for the Lie algebra of Hamiltonian vector fields on a torus, which admit a compatible action for the commutative algebra of multivariate Laurent polynomials are called category $\mathcal{J}$. This paper classifies the indecomposable and the irreducible modules in category $\mathcal{J}$.