Lie super-bialgebra structures on the two dimensional supersymmetric Galilean conformal algebra

Abstract

Let $\mathcal{G}$ be the two dimensional supersymmetric Galilean conformal algebra. In this paper, we obtain that Lie superalgebra $\mathcal{G}$ admits only triangular coboundary Lie super-bialgebra structures and the proof is mainly based on the computation of the first cohomology group of $\mathcal{G}$ with coefficients in the tensor product of its adjoint module.

KEYWORDS:

• Lie super-bialgebra structures
• the two dimensional supersymmetric Galilean conformal algebra

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B05
• 17B40
• 17B68

Additional information

Funding

J.-C. Sun would like to thank the support of National Natural Science Foundation of China10.13039/501100001809 (Nos. 12071276, 11931009 and 12226402).