Local properties of Schrödinger-Virasoro type Lie algebras and a full diamond thin Lie algebra

Abstract

Let $\mathcal{S}\mathcal{V}(z)$ be a class of Schrödinger-Virasoro type Lie algebras, where $z\in \mathbb{Z}$. In this paper, we show that $\mathcal{S}\mathcal{V}(z)$ is 2-local complete (namely, every 2-local derivation is a derivation) for almost all integers z’s. We also introduce the notion of full diamond thin Lie algebras, and construct an example $\mathcal{F}$ from $\mathcal{S}\mathcal{V}(-1)$. We completely determine the derivations of $\mathcal{F}$ by combinatoric techniques, and show that $\mathcal{F}$ is not 2-local complete.

Keywords:

• 2-local complete
• 2-local derivation
• Schrödinger-Virasoro type Lie algebras
• thin Lie algebras

2020 Mathematics Subject Classification:

• 17B40
• 17B65
• 17B68

Acknowledgments

We are very grateful to the referee for helpful comments that have improved the manuscript.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 12371025).