Biderivations, linear commuting maps and commutative post-Lie algebra structures on W-algebras

ABSTRACT

In this paper, the biderivations without the skew-symmetric condition of W-algebras including the Witt algebra, the algebra W(2,2) and their central extensions are characterized. Some classes of non-inner biderivations are presented. As applications, the forms of linear commuting maps and the commutative post-Lie algebra structures on aforementioned W-algebras are given.

KEYWORDS:

• Biderivation
• linear commuting map
• post-Lie algebra
• W-algebra

AMS SUBJECT CLASSIFICATION:

• 17B05
• 17B40
• 17B68

Acknowledgments

I am very grateful to the referee for his (or her) valuable suggestions and comments, in particular, providing me Lemmas 1.1, 1.2 and 4.5 makes our proof to be simplified. I also thank Prof. Yufeng Pei for helpful discussions.