We show that a recently proposed action for three-dimensional non-relativistic gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the coadjoint Poincaré algebra. We point out the similarity of our construction with the way that three-dimensional Galilei gravity and extended Bargmann gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the Poincaré algebra. We extend our results to the anti-de Sitter case and we will see that there is a chiral decomposition at both the relativistic and non-relativistic level. We comment on possible further generalizations.

中文翻译：

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非相对论极限和三维共伴随庞加莱引力

我们表明，最近提出的三维非相对论引力作用可以通过采用涉及共伴随 Poincaré 代数的相对论拉格朗日的极限来获得。我们指出我们的构造与通过采用涉及庞加莱代数的相对论拉格朗日的极限来获得三维伽利略引力和扩展巴格曼引力的方式的相似性。我们将我们的结果扩展到反德西特案例，我们将看到在相对论和非相对论水平上都存在手性分解。我们评论可能的进一步概括。