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Journal of Lie Theory 28 (2018), No. 4, 903--914
Copyright Heldermann Verlag 2018

Category J Modules for Hamiltonian Vector Fields on a Torus

John Talboom
Dept. of Mathematics, Trent University, 1600 West Bank Drive, Peterborough, Ontario, Canada K9L 0G2

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, and have finite dimensional weight spaces, are called category J. This paper classifies the indecomposable and the irreducible modules in category J.

Keywords: Indecomposable representations, irreducible representations, Lie algebra of Hamiltonian vector fields, weight module.

MSC: 17B10, 17B66

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