Parabolic geometries determined by filtrations of the tangent bundle

Sagerschnig, Katja. "Parabolic geometries determined by filtrations of the tangent bundle." Proceedings of the 25th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2006. [175]-181. <http://eudml.org/doc/221255>.

@inProceedings{Sagerschnig2006,
abstract = {Summary: Let $\{\mathfrak \{g\}\}$ be a real semisimple $|k|$-graded Lie algebra such that the Lie algebra cohomology group $H^1(\{\mathfrak \{g\}\}_-,\{\mathfrak \{g\}\})$ is contained in negative homogeneous degrees. We show that if we choose $G= \operatorname\{Aut\}(\{\mathfrak \{g\}\})$ 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 $\text\{gr\}(T_xM)$ is isomorphic to the graded Lie algebra $\{\mathfrak \{g\}\}_-$. Examples of parabolic geometries determined by filtrations of the tangent bundle are discussed.},
author = {Sagerschnig, Katja},
booktitle = {Proceedings of the 25th Winter School "Geometry and Physics"},
location = {Palermo},
pages = {[175]-181},
publisher = {Circolo Matematico di Palermo},
title = {Parabolic geometries determined by filtrations of the tangent bundle},
url = {http://eudml.org/doc/221255},
year = {2006},
}

TY - CLSWK
AU - Sagerschnig, Katja
TI - Parabolic geometries determined by filtrations of the tangent bundle
T2 - Proceedings of the 25th Winter School "Geometry and Physics"
PY - 2006
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [175]
EP - 181
AB - Summary: Let ${\mathfrak {g}}$ be a real semisimple $|k|$-graded Lie algebra such that the Lie algebra cohomology group $H^1({\mathfrak {g}}_-,{\mathfrak {g}})$ is contained in negative homogeneous degrees. We show that if we choose $G= \operatorname{Aut}({\mathfrak {g}})$ 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 $\text{gr}(T_xM)$ is isomorphic to the graded Lie algebra ${\mathfrak {g}}_-$. Examples of parabolic geometries determined by filtrations of the tangent bundle are discussed.
UR - http://eudml.org/doc/221255
ER -