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On Automorphisms with Natural Tangent Actions on Homogeneous Parabolic Geometries

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GREGOROVIČ Jan ZALABOVÁ Lenka

Rok publikování 2015
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Lie Theory
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
Obor Obecná matematika
Klíčová slova Parabolic geometries; homogeneous spaces; automorphisms with fixed points; harmonic curvature restrictions
Popis We consider automorphisms of homogeneous parabolic geometries with a fixed point. Parabolic geometries carry the distinguished distributions and we study those automorphisms which enjoy natural actions on the distributions at the fixed points. We describe the sets of such automorphisms on homogeneous parabolic geometries in detail and classify whether there are non flat homogeneous parabolic geometries carrying such automorphisms. We present two general constructions of such geometries and we provide complete classifications for the types (G, P) of the parabolic geometries that have G simple and the automorphisms are of order 2.
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