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arXiv · 2303.08180

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

Yang Yang·Xiaomin Tang·Abror Khudoyberdiyev
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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 $n\neq 2$ 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 Schrödinger algebra $\mathcal{S}_{2}$ admits a non-trivial ${\rm Hom}$-Lie structure.

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Yang Yang, Xiaomin Tang, Abror Khudoyberdiyev. 2023-03-02. Transposed Poisson structures on Schrodinger algebra in (n+1)-dimensional space-time. https://arxiv.org/abs/2303.08180

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