对数泊松上同调：计算和应用于预量子化的例子
Logarithmic Poisson cohomology: example of calculation and application to prequantization
摘要：
本文引入了对数Poisson结构和对数主Poisson结构的概念，证明了后者导出了对数Kahler微分模的对数导子表示，从而导出了一个微分复形，并由此导出了对数Poisson上同调的概念.证明了当Poisson结构为对数辛时，Poisson上同调与对数Poisson上同调是等价的。我们给出了一个非对数辛但对数泊松结构的例子，这些上同调是相等的。我们还给出了一个例子，这些上同调是不同的。讨论并修正了K. Saito对数形式的定义。注释以对数泊松代数的预量化的应用结束：（C[x; y]; {x; y} = x）：
英文摘要：
In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notion of logarithmic Poisson cohomology. We prove that Poisson cohomology and logarithmic Poisson cohomology are equal when the Poisson structure is logsymplectic. We give an example of non logsymplectic but logarithmic Poisson structure for which these cohomologies are equal. We also give an example for which these cohomologies are different. We discuss and modify the K. Saito definition of logarithmic forms. The notes end with an application to a prequantization of the logarithmic Poisson algebra: (C[x; y]; {x; y} = x):
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
