Biderivations of the planar Galilean conformal algebra and their applications

ABSTRACT

In this paper, the biderivations without skew-symmetric condition of the planar Galilean conformal algebra are presented. As applications, the characterizations of the forms of linear commuting maps and the commutative post-Lie algebra structures on the planar Galilean conformal algebra are given.

KEYWORDS:

• Biderivation
• planar Galilean conformal algebra
• linear commuting map
• post-Lie algebra

AMS SUBJECT CLASSIFICATIONS:

• 17B05
• 17B40
• 17B65

Acknowledgements

We are very grateful to the referees and editor for their invaluable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 11771069], [grant number 11701158]; the Natural Science Foundation of Heilongjiang Province [grant number A2015007] and the Fund of the Heilongjiang Education Committee [grant number 12531483], [grant number HDJCCX-2016211].