Left-symmetric superalgebra structures on the super Galilean conformal algebra

Abstract

The compatible left-symmetric superalgebra structures on the super Galilean conformal algebra with some natural grading conditions are completely determined. The results of earlier work on left-symmetric superalgebra structures on the infinite-dimensional Lie superalgebra $\mathfrak{g}$ studied by Chen and Hassan play an essential role in determining these compatible structures.

KEYWORDS:

• Infinite-dimensional Lie superalgebra
• left-symmetric superalgebra
• super Galilean conformal algebra

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B65
• 17B68
• 17B70
• 17D25

Acknowledgments

I want to thank my advisor Prof. Hongjia Chen for helpful comments to correct some inaccuracies and make the paper more readable. I would like to express my gratitude to the Chinese government for its generous support. I would also like to thank the referee for helpful suggestions which improved the exposition of this paper.

Additional information

Funding

This paper is partially supported by the NSF of China (11931009, 12161141001, 12171132 and 11771410) and Innovation Program for Quantum Science and Technology (2021ZD0302902).