泊松流形的皮卡群
微分几何
2016-04-11 v3 辛几何
摘要
对于泊松流形 ，我们发展了计算其皮卡群 （即其自莫里塔等价群）的系统性方法。我们建立了 与模泊松微分同胚的规范变换群之间的精确关系，特别地表明它们的恒等连通分支重合；这使我们能够引入 的皮卡李代数并研究其基本性质。我们的方法尤其导致了 [BW04] 中一个猜想的证明，该猜想陈述：对任意紧单李代数 ，群 与 的外自同构群重合。
引用
@article{arxiv.1509.03780,
title = {Picard groups of Poisson manifolds},
author = {Henrique Bursztyn and Rui Loja Fernandes},
journal= {arXiv preprint arXiv:1509.03780},
year = {2016}
}
备注
A few typos were corrected and some clarifications were made, based on a referee report. The proof of the fact that the group of gauge transformations up to Poisson diffeomorphisms yields a normal subgroup of the Picard group was added. Final version accepted for publication in J. Diff. Geometry