Representations of super deformation of Heisenberg-Virasoro type Lie conformal algebras

Abstract

We introduce a class of Lie conformal superalgebra S(a, b), where a, b are complex parameters. These Lie conformal superalgebras can be viewed as the super deformation of Heisenberg-Virasoro type Lie conformal algebras. We classify the free conformal modules of rank $(1+1)$ over S(a, b) for all $a,b\in \mathbb{C}$. Using a Cheng-Kac’s lemma, we also classify the finite irreducible conformal modules over S(a, b).

KEYWORD:

• Conformal module
• Heisenberg-Virasoro conformal algebra
• Lie conformal superalgebra

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B10
• 17B65
• 17B68
• 17B69

Acknowledgments

We thank the referee for helpful suggestions.

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central University, China (2019QNA34).