Super-biderivations and super-commuting maps on the super Galilean conformal algebras

ABSTRACT

Let 𝔤 be the super Galilean conformal algebra. In this paper, we first determine all the super-skewsymmetric super-biderivations of 𝔤. In particular, we find that there exist non-inner super-biderivations of 𝔤. Based on the result of super-biderivations, we show that all the linear super-commuting maps on 𝔤 are standard.

KEYWORDS:

• Super-biderivations
• super-commuting maps
• super Galilean conformal algebras

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B05
• 17B40
• 17B68

Acknowledgment

We would like to thank the referee for careful reading of the manuscript and for valuable comments and suggestions.