论文标题
符号动作和中央扩展
Symplectic Actions and Central Extensions
论文作者
论文摘要
我们给出了一个事实证明，一个相互连接的Lie Group $ G $的简单连接的符号均匀空间$（m，ω）$是$ g $的一维中心扩展名的共同封面。我们强调了符合群体的共生的ro和这种Cocycles，左右的左右$ g $和中央扩展名的关系之间的关系；特别是，我们表明，$ \ mathfrak {g} $的中心扩展到$ g $的中心扩展相当于代表性的chevalley-eilenberg 2 cocycle的可集成性，即$ \ mathfrak {g} $的cocyclecyclecycle $ g $ $ g $。
We give a proof of the fact that a simply-connected symplectic homogeneous space $(M,ω)$ of a connected Lie group $G$ is the universal cover of a coadjoint orbit of a one-dimensional central extension of $G$. We emphasise the rôle of symplectic group cocycles and the relationship between such cocycles, left-invariant presymplectic structures on $G$ and central extensions of $G$; in particular, we show that integrability of a central extension of $\mathfrak{g}$ to a central extension of $G$ is equivalent to integrability of a representative Chevalley-Eilenberg 2-cocycle of $\mathfrak{g}$ to a symplectic cocycle of $G$.
