Hasse diagrams for parabolic geometries

Krump, Lukáš; Souček, Vladimír

BGG diagrams for contact graded odd dimensional orthogonal geometries

Svatopluk Krýsl (2004)

Acta Universitatis Carolinae. Mathematica et Physica

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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...

Displaying similar documents to “Hasse diagrams for parabolic geometries”

BGG diagrams for contact graded odd dimensional orthogonal geometries

Parabolic geometries determined by filtrations of the tangent bundle