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Transposed Poisson structures on Schrodinger algebra in (n+1)-dimensional space-time (2303.08180v1)

Published 2 Mar 2023 in math.RA

Abstract: Transposed Poisson structures on the Schr\"{o}dinger algebra in $(n+1)$-dimensional space-time of Schr\"{o}dinger Lie groups are described. It was proven that the Schr\"{o}dinger algebra $\mathcal{S}{n}$ in case of $n\neq 2$ 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 Schr\"{o}dinger algebra $\mathcal{S}_{2}$ admits a non-trivial ${\rm Hom}$-Lie structure.

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