标题： 最后乘子用于多向量及其在泊松几何中的应用 显示英文标题

标题： Last multipliers for multivectors with applications to Poisson geometry

摘要： 最后乘子理论作为Liouville输运方程的解，之前针对向量场开发的，现在扩展到一般的多向量。 以Witten和Marsden微分形式的表征也被重新获得，以及具有共同最后乘子的多向量集合的代数结构，即Gerstenhaber代数。 通过获得最后乘子来计算给定体积形式下泊松结构偏离精确的程度，展示了对泊松双矢的应用。 引入了在$IR^{n}$上单模泊松结构的精确泊松上同调的概念。 显示英文摘要

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.