Year: 2022
Type: preprint
Abstract: 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 $G$.
Source: arXiv (Cornell University)
Authors: Beckett, Andrew, Figueroa-O'Farrill, José
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4226073853