Transposed Poisson Structures on Schrödinger Algebra in (n+1)-Dimensional Space-Time

This paper investigates the transposed Poisson structures on the Schrödinger algebra [Formula: see text] associated with [Formula: see text]-dimensional space-time of the Schrödinger Lie group. We prove that for [Formula: see text], the algebra [Formula: see text] admits no nontrivial [Formula: see text]-derivations and, consequently, no nontrivial transposed Poisson structures. In contrast, for the case [Formula: see text], we explicitly determine all [Formula: see text]-derivations and the corresponding transposed Poisson structures on [Formula: see text]. Additionally, we demonstrate that [Formula: see text] admits a nontrivial Hom-Lie structure.