Biderivations of q-deformed Heisenberg–Virasoro algebras

Abstract

In this article, we compute biderivations of the q-deformed Heisenberg–Virasoro algebra. As an application, linear commuting maps are characterized. We also provide calculations of α-derivations and α-biderivations of the q-deformed Heisenberg–Virasoro algebra and obtain that it has no nonzero α-derivations and α-biderivations.

Keywords:

• α-Biderivations
• α-derivations
• biderivations
• Hom–Lie algebras
• linear commuting maps
• q-deformed Heisenberg–Virasoro algebra

2020 Mathematics Subject Classification:

• 17A30
• 17A60
• 17B05
• 17B60
• 17B70

Additional information

Funding

This work was supported by National Natural Science Foundation grants of China (grant number: 11301109).