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Abstract
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The Lie algebra of divergence zero vector fields on a torus is an infinite-dimensional
Lie algebra of skew derivations over the ring of Laurent polynomials. We consider the
semidirect product of the Lie algebra of divergence zero vector fields on a torus with
the algebra of Laurent polynomials. In this paper, we prove that a Harish-Chandra
module of the universal central extension of the derived Lie subalgebra of this
semidirect product is either a uniformly bounded module or a generalized highest
weight module. We also classify all the generalized highest weight Harish-Chandra
modules.
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Keywords
Harish-Chandra, divergence zero vector fields, generalized
highest weight module
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Mathematical Subject Classification 2010
Primary: 17B10, 17B66
Secondary: 17B65, 17B68
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Milestones
Received: 8 July 2018
Revised: 26 October 2018
Accepted: 29 November 2018
Published: 16 September 2019
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