论文标题
同质符号空间和中央扩展
Homogeneous Symplectic Spaces and Central Extensions
论文作者
论文摘要
我们总结了Kirillov的经典结果，总结了最近的工作（Arxiv：2203.07405 [Math.sg]），即连接组的$ G $的任何简单连接的同质均匀空间是Hamiltonian $ \ wideHat {g wideHat {g} $ \ g} $ \ g $ g $ g $ g $ g}的空间KOSTANT）$ \ wideHat {g} $的coadexhixhine轨道的封面。我们强调，文献中的现有证据假设$ g $是简单连接的，并且可以通过应用NEEB定理来删除此假设。我们还将NEEB的定理解释为将Lie代数的一维中心扩展与相关的Chevalley-Eilenberg 2 Cocycle的整合性相关联。
We summarise recent work (arXiv:2203.07405 [math.SG]) on the classical result of Kirillov that any simply-connected homogeneous symplectic space of a connected group $G$ is a hamiltonian $\widehat{G}$-space for a one-dimensional central extension $\widehat{G}$ of $G$, and is thus (by a result of Kostant) a cover of a coadjoint orbit of $\widehat{G}$. We emphasise that existing proofs in the literature assume that $G$ is simply-connected and that this assumption can be removed by application of a theorem of Neeb. We also interpret Neeb's theorem as relating the integrability of one-dimensional central extensions of Lie algebras to the integrability of an associated Chevalley--Eilenberg 2-cocycle.
