Biderivations of the extended Schrödinger-Virasoro Lie algebra

Abstract

Let $ \widetilde{\mathfrak{sv}} $ be the extended Schrödinger-Virasoro Lie algebra. In this paper, we consider the skew-symmetric biderivations of the extended Schrödinger-Virasoro Lie algebra. We prove that all biderivations of $ \widetilde{\mathfrak{sv}} $ are inner. Based on this result, we show that all linear commuting maps on $ \widetilde{\mathfrak{sv}} $, which have the form $ \psi(x) = \lambda x $, are standard.

Keywords

• extended schrödinger-virasoro lie algebra
• biderivation
• skew-symmetric
• inner biderivation
• linear commuting map