δ-(bi)derivations and transposed Poisson algebra structures on the n-th Schrödinger algebra

Abstract

The [Formula: see text]-th Schrödinger algebra [Formula: see text] is the semidirect product of the Lie algebra [Formula: see text] with the [Formula: see text]-th Heisenberg Lie algebra [Formula: see text]. In this paper, we will show that [Formula: see text] has neither nontrivial [Formula: see text]-derivations nor nontrivial transposed Poisson algebra structures, and doesn’t have nonzero [Formula: see text]-biderivations. In addition, all [Formula: see text]-derivations and [Formula: see text]-biderivations on [Formula: see text] are all described.