What question did this study set out to answer?

This research aims to explore transposed Poisson structures in the context of the Schrödinger algebra related to space-time.

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February 28, 2026

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

Key Points

This research aims to explore transposed Poisson structures in the context of the Schrödinger algebra related to space-time.
Analytical examination of Schrödinger algebra properties
Derivation of nontrivial Poisson structures
Determination of all derivations in specific cases
No nontrivial derivations were found for certain scenarios.
Explicit determination of all derivations and Poisson structures for other cases.
Existence of a nontrivial Hom-Lie structure in the algebra was demonstrated.

Abstract

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.

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Cite This Study

Yang et al. (Fri,) studied this question.

synapsesocial.com/papers/69a288060a974eb0d3c03f1d https://doi.org/https://doi.org/10.1142/s1005386726000131

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