Biderivations of the extended Schrödinger-Virasoro Lie algebra

Abstract

<abstract><p>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.</p></abstract>