Some Representations of Nongraded Divergence-Free Lie Algebras

Abstract

Divergence-free Lie algebras are originated from the Lie algebras of volume-preserving transformation groups. Xu constructed a certain nongraded generalization, which may not contain any toral Cartan subalgebra. 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.