The derivation algebra and automorphism group of the n-th Schrödinger algebra

Abstract

The n-th Schrödinger algebra is the semidirect product of the special linear Lie algebra $\mathfrak{s}{\mathfrak{l}}_2$ and the Heisenberg algebra ${\mathfrak{h}}_n$. In this paper, we describe explicitly the structure of the derivation algebra and automorphism group of the n-th Schrödinger algebra. Especially, the automorphism group of the Schrödinger algebra is obtained.

Keywords:

• Automorphism group
• derivation algebra
• the n-th Schrödinger algebra

2020 Mathematics Subject Classification:

• 17B05
• 17B40
• 17B56

Acknowledgments

Hengyun Yang is grateful to professor Yanan Cai for providing the undergraduate thesis of his student, where the automorphism group of the electrical Lie algebra of type G₂ was given, and for his expert advice.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 12071276).