2005/08/26 by Andreas Čap, Andreas Cap, Vladimı́r Souček +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebra over a field #Differential operator #Flatness (cosmology) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Hypersurface #Invariant (physics) #Mathematical physics #Mathematics #Physics #Pure mathematics #Torsion (gastropod) #Type (biology) #math.CV #math.DG #msc:32V05 #msc:53A40 #msc:53B15 #msc:53C15 #msc:53D10 #msc:58J10
paper · pdf · doi:10.1007/s00208-011-0726-4
published as Math. Ann. 354, No. 1 (2012) 111-136 · 29 pages, no figures
arxiv created 2005/08/26 · openalex publication_date 2011/10/10 · arxiv updated 2012/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
BGG-sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the compositions of the operators in such a sequence are nonzero. In this paper, we show that under appropriate torsion freeness and/or semi-flatness assumptions certain parts of all BGG sequences are complexes. Several examples of structures, including quaternionic structures, hypersurface type CR structures and quaternionic contact structures are discussed in detail. In the case of quaternionic structures we show that several families of complexes obtained in this way are elliptic.