Abstract
We study the automorphism group of a Cartan geometry, and prove an embedding theorem analogous to a result of Zimmer for automorphism groups of G-structures. Our embedding theorem leads to general upper bounds on the real rank or nilpotence degree of a Lie subgroup of the automorphism group. We prove that if the maximal real rank is attained in the automorphism group of a geometry of parabolic type, then the geometry is flat and complete.
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