An embedding theorem for automorphism groups of Cartan geometries

Details An embedding theorem for automorphism groups of Cartan geometries An embedding theorem for automorphism groups of Cartan geometries

2007-09-24

arxiv.org/abs/0709.3844v1

Mathematics

Differential Geometry

33 pages

Scientific paper

We prove a theorem relating the automorphism group of a Cartan geometry to the group on which the geometry is modeled: a component of the adjoint representation of the first embeds in the adjoint representation of the second. Consequences of the theorem include general bounds on the rank and nilpotence degree of an automorphism group; a result asserting local homogeneity and completeness of parabolic geometries admitting a maximal-rank group of automorphisms; and a local freeness theorem for actions additionally preserving a continuous volume form.

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