ABSTRACT
For the two Cartan type S subalgebras of the Witt algebra 𝒲n, called Lie algebras of divergence-zero vector fields, we determine all module structures on the universal enveloping algebra of their Cartan subalgebra 𝔥n. We also give all submodules of these modules.
Acknowledgment
Sincere thanks should go to Professor Kaiming Zhao for formulating the problem and stimulating discussions, for his keen guidance and good advices on the paper. Special thanks should also go to Professor Xiandong Wang for his patient discussions.