Parabolic geometries determined by filtrations of the tangent bundle

Proceedings of the 25th Winter School "Geometry and Physics", GDML_Books, (2006), p. [175]-181 / Harvested from

Résumé

Summary: Let $𝔤$ be a real semisimple $| k |$ -graded Lie algebra such that the Lie algebra cohomology group $H^{1} (𝔤_{-}, 𝔤)$ is contained in negative homogeneous degrees. We show that if we choose $G = Aut (𝔤)$ and denote by $P$ the parabolic subgroup determined by the grading, there is an equivalence between regular, normal parabolic geometries of type $(G, P)$ and filtrations of the tangent bundle, such that each symbol algebra $gr (T_{x} M)$ is isomorphic to the graded Lie algebra $𝔤_{-}$ . Examples of parabolic geometries determined by filtrations of the tangent bundle are discussed.

MR MR2287136 | Zbl 1114.53029

EUDML-ID : urn:eudml:doc:221255
Mots clés:

@article{701776,
     title = {Parabolic geometries determined by filtrations of the tangent bundle},
     booktitle = {Proceedings of the 25th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2006},
     pages = {[175]-181},
     mrnumber = {MR2287136},
     zbl = {1114.53029},
     url = {http://dml.mathdoc.fr/item/701776}
}

Sagerschnig, Katja. Parabolic geometries determined by filtrations of the tangent bundle, dans Proceedings of the 25th Winter School "Geometry and Physics", GDML_Books,  (2006), pp. [175]-181. http://gdmltest.u-ga.fr/item/701776/