Non-weight representations of Cartan type S Lie algebras

ABSTRACT

For the two Cartan type S subalgebras of the Witt algebra 𝒲_n, called Lie algebras of divergence-zero vector fields, we determine all module structures on the universal enveloping algebra of their Cartan subalgebra 𝔥_n. We also give all submodules of these modules.

KEYWORDS:

• Lie algebras of Cartan type S
• Lie algebras of divergence-zero vector fields
• non-weight modules
• Virasoro-like algebra

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B10
• 17B20
• 17B65
• 17B66
• 17B68

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.