Transposed Poisson structures on Schrodinger algebra in (n+1)-dimensional space-time

Abstract

Transposed Poisson structures on the Schrödinger algebra in $(n+1)$-dimensional space-time of Schrödinger Lie groups are described. It was proven that the Schrödinger algebra ${\mathcal{S}}_n$ in case of $n\ne 2$ does not have non-trivial $\frac{1}{2}$-derivations and as it follows it does not admit non-trivial transposed Poisson structures. All $\frac{1}{2}$-derivations and transposed Poisson structures for the algebra ${\mathcal{S}}_2$ are obtained. Also, we proved that the Schrödinger algebra ${\mathcal{S}}_2$ admits a non-trivial $\mathrm{Hom}$-Lie structure.

16 pages