Local δ-derivations of n-th Schrödinger algebras

Let [Formula: see text] be a field, [Formula: see text] a Lie algebra over [Formula: see text], [Formula: see text]. A [Formula: see text]-derivation on [Formula: see text] is a linear map [Formula: see text] which satisfies that [Formula: see text] for all [Formula: see text] and a local [Formula: see text]-derivation on [Formula: see text] is a linear map [Formula: see text] which satisfies that for any [Formula: see text], there exists a [Formula: see text]-derivation [Formula: see text] (depending on [Formula: see text]) such that [Formula: see text] In this paper, we prove that any local one-derivation (i.e. local derivation) of the [Formula: see text]-th Schrödinger algebra [Formula: see text] is a derivation, any local [Formula: see text]-derivation of [Formula: see text] is a scalar multiplication map, and for [Formula: see text] or [Formula: see text], any local [Formula: see text]-derivation is zero, where [Formula: see text] is the semi-direct product of the Lie algebra [Formula: see text] with the [Formula: see text]-th Heisenberg Lie algebra [Formula: see text].