Poisson Structures and Lie Algebra Cohomology

摘要 提案：DMS-9803624主要研究者：Jiang-Hua Lu 这个项目是关于应用泊松几何拓扑和李理论。具体地说，我们建议研究等变上同调旗流形上使用某些泊松结构。 这也应该产生结果的李代数上同调的幂零李代数。部分结果已经报道在一份联合文件与山姆埃文斯在其中我们给泊松几何解释的Kostant调和形式的旗帜流形。 泊松结构起源于物理学，第一个由法国数学家S. D.泊松在1809年研究经典力学时。后来，挪威数学家S.撒谎如今，它在物理学，控制理论，加工自动化和机器人操作中得到应用。

Abstract Proposal: DMS-9803624 Principal Investigator: Jiang-Hua Lu This project is about applications of Poisson geometry to topology and to Lie theory. Specifically, we propose to study equivariant cohomology of flag manifolds using certain Poisson structures on them. This should also yield results on the Lie algebra cohomology of nilpotent Lie algebras. Partial results have already been reported in a joint paper with Sam Evens in which we give Poisson geometrical interpretation of the Kostant harmonic forms on flag manifolds. Poisson structures arise from physics, the first one being written down by the French mathematician S.D. Poisson in 1809 when studying classical mechanics. Subsequently they were investigated by the Norwegian mathematician S. Lie. Nowadays, it finds applications in physics, control theory, machining automation and robotic manipulation.