2022/03/14 by Andrew Beckett, Beckett, Andrew, José Figueroa-O’Farrill +1 · 1 citation
Mathematics · #22E60 #53D20 #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2203.07405
openalex publication_date 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \mathfrakg to a central extension of G is equivalent to integrability of a representative Chevalley-Eilenberg 2-cocycle of \mathfrakg to a symplectic cocycle of G.