Biderivations And Linear Commuting Maps on the Schrödinger-Virasoro Lie Algebra

Abstract

Let 𝔏 be the Schrdinger–Virasoro Lie algebra over the complex field ℂ. In this article, we prove that each biderivation of 𝔏 is inner. As an application of biderivations, we show that every linear commuting map ψ on 𝔏 has the form ψ(x) = λx + f(x)M ₀, where λ ∈ ℂ, M ₀ is a basis of the one-dimensional center of 𝔏, and f is a linear function from 𝔏 to ℂ.

Key Words:

• Biderivations
• Commuting maps
• Schrödinger–Virasoro Lie algebra

2010 Mathematics Subject Classification:

• 17B05
• 17B20
• 17B30
• 17B40

ACKNOWLEDGMENT

The authors thank the referee for his (or her) careful examination and helpful suggestions.

Supported by “the Fundamental Research Funds for the Central Universities (2012LWA08);” and “the National Natural Science Foundation of China (No. 11171343).”

Notes

Communicated by M. Bresar.