Irreducible Modules for the Lie Algebra of Divergence Zero Vector Fields\n on a Torus

2014/11/14 by John Talboom, Talboom, John · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1411.4087

openalex publication_date 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the irreducibility of certain representations for the\nLie algebra of divergence zero vector fields on a torus. In "Irreducible\nRepresentations of the Lie-Algebra of the Diffeomorphisms of a d-Dimensional\nTorus," S. Eswara Rao constructs modules for the Lie algebra of polynomial\nvector fields on a d-dimensional torus, and determines the conditions for\nirreducibility. The current paper considers the restriction of these modules to\nthe subalgebra of divergence zero vector fields. It is shown here that Rao's\nresults transfer to similar irreducibility conditions for the Lie algebra of\ndivergence zero vector fields.\n

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• Uniformly bounded weight modules for Map extended Special and Map extended Hamiltonian Lie algebras
• Tensor modules over the Lie algebras of divergence zero vector fields on ℂⁿ

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• Classification of Category J Modules for Divergence Zero Vector Fields on a Torus
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