Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides a suitable framework for the study of the Hamiltonization problem for the linearized dynamics along Poisson submanifolds.

中文翻译：

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无限小泊松代数和哈密顿系统的线性化

使用逆变导数的概念，我们给出了与泊松子流形的无穷小数据相关的泊松代数的一些代数和几何特征。我们表明，这样一类泊松代数为研究沿泊松子流形的线性动力学的哈密顿化问题提供了合适的框架。