Displaying similar documents to “Remarks on Grassmannian Symmetric Spaces”

Remarks on symmetries of parabolic geometries

Lenka Zalabová (2006)

Archivum Mathematicum

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We consider symmetries on filtered manifolds and we study the | 1 | -graded parabolic geometries in more details. We discuss the existence of symmetries on the homogeneous models and we conclude some simple observations on the general curved geometries.

Parabolic geometries determined by filtrations of the tangent bundle

Sagerschnig, Katja

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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...