Derivations and Biderivations of the Schrödinger algebra in (n + 1)-dimensional space-time

Abstract

In this paper, all derivations of the Schrödinger algebra in $(n+1)$-dimensional space-time of the Schrödinger Lie group are determined. As applications, all biderivations are obtained. Finally, as applications of biderivations, the linear commuting maps and commutative post-Lie algebra structures on this algebra are given.

Keywords:

• Schrödinger algebra
• derivation
• biderivations
• linear commuting map
• post-Lie algebra

Mathematics Subject Classifications:

• 17A32
• 17B30
• 17B10

Acknowledgments

We would like to thank the referee for invaluable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported in part by National Natural Science Foundation of China [grant number 11771069], Natural Science Foundation of Heilongjiang Province [grant number LH2020A020] and the Found for the graduate innovation research of Heilongjiang University [grant number YJSCX2021-211HLJU].