多向量的最后乘子及其在Poisson几何中的应用
Last multipliers for multivectors with applications to Poisson geometry
摘要：
最后的乘数作为解决方案的刘维尔的输运方程，以前开发的向量场的理论，在这里扩展到一般的多向量。重新得到了Witten微分和Marsden微分的刻画以及具有公共最后乘子的多向量集的代数结构，即Gerstenhaber代数。泊松双向量的应用程序获得的最后乘数计数的“多远”是一个泊松结构是准确的相对于一个给定的体积形式。对$IR^{n}$上的单模Poisson结构引入了精确Poisson上同调的概念.
英文摘要：
The theory of the last multipliers as solutions of the Liouville's transport equation, previously developed for vector fields, is extended here to general multivectors. Characterizations in terms of Witten and Marsden differentials are reobtained as well as the algebraic structure of the set of multivectors with a common last multiplier, namely Gerstenhaber algebra. Applications to Poisson bivectors are presented by obtaining that last multipliers count for ''how far away'' is a Poisson structure from being exact with respect to a given volume form. The notion of exact Poisson cohomology for an unimodular Poisson structure on $IR^{n}$ is introduced.
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