Non-weight representations of Cartan type H Lie algebras

Abstract

In this article, we classify the ${\mathbf{H}}_n$-modules satisfying (1.3), and find the only irreducible submodules of them.

Keywords:

• Lie algebras of Cartan type H
• Lie algebras of Cartan type S
• non-weight modules
• Witt algebra

2000 MATHEMATICS SUBJECT CLASSIFICATION:

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

Acknowledgements

Sincere thanks should go to Professor Kaiming Zhao for formulating the problem and stimulating discussions, for his keen guidance and good advices on the article. Special thanks should also go to Professor Xiandong Wang for his patient discussions.

Additional information

Funding

The author is partially supported by NSFC (Grant No.11472144), NSFC (Grant No.11501315) and a Project of Shandong Province Higher Educational Science and Technology Program (J14LI10).