$n$-Derivations of the Extended Schrödinger–Virasoro Lie Algebra

Let $\widetilde{\mathfrak{s}\mathfrak{v}}$ be the extended Schrödinger–Virasoro Lie algebra and $n\ge 1$ an integer. A map $f:{\widetilde{\mathfrak{s}\mathfrak{v}}}^n=\widetilde{\mathfrak{s}\mathfrak{v}}\times \widetilde{\mathfrak{s}\mathfrak{v}}\times \cdots \times \widetilde{\mathfrak{s}\mathfrak{v}}\to \widetilde{\mathfrak{s}\mathfrak{v}}$ is called an $n$-derivation if it is a derivation in one variable while other variables fixed. We investigate $n$-derivations of the extended Schrödinger–Virasoro Lie algebra $\widetilde{\mathfrak{s}\mathfrak{v}}$. The main result when $n=2$ is then applied to characterize the linear commuting maps and the commutative post-Lie algebra structures on $\widetilde{\mathfrak{s}\mathfrak{v}}$.