Biderivations of the deformative Schrödinger-Virasoro algebras

Abstract

For $a,b\in \mathbb{C}$, s = 0 or $\frac{1}{2}$, the deformative Schrödinger-Virasoro algebra $\mathcal{W}(a,b,s)$ is the semi-direct product Lie algebra of the Witt algebra and its tensor density module. It contains W-algebra $\mathcal{W}(a,b)$ as its subalgebras, and Schrödinger-Virasoro algebra is his special case. In this paper, all biderivations of $\mathcal{W}(a,b,s)$ are determined. It is observed that these Lie algebras have rich variety of symmetric (and skewsymmetric) non-inner biderivations. As an application, commutative post-Lie algebra structures on $\mathcal{W}(a,b,s)$ are obtained.

Keywords:

• Biderivation
• deformative Schrödinger-Virasoro algebra
• post-Lie algebra

AMS SUBJECT CLASSIFICATIONS:

• 17B05
• 17B40
• 17B65

Acknowledgments

We are very grateful to the referee for his (or her) valuable suggestions and comments, in particular, providing us Lemma 1.1.

Additional information

Funding

This work was supported in part by the NNSFC (grant number 11171294) and the fund of Heilongjiang Provincial Laboratory of the Theory and Computation of Complex Systems.