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Journal of Lie Theory 23 (2013), No. 2, 507--549
Copyright Heldermann Verlag 2013

Generalized Multiplicity-Free Representations of Nongraded Divergence-Free Lie Algebras

Ling Chen
Beijing International Center for Mathematical Research, Peking University, Beijing 100871, P. R. China

Divergence-free Lie algebras originate from the Lie algebras of volume-preserving transformation groups. Xu constructed a certain nongraded generalization, which do not contain any toral Cartan subalgebra in generic case. In this paper, we give a complete classification of the generalized weight modules over these algebras with weight multiplicities less than or equal to one.

Keywords: Divergence-free Lie algebra, Cartan type, irreducible module, generalized weight module, classification.

MSC: 17B10, 17B65

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