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An Embedding Theorem for Automorphism Groups of Cartan Geometries |
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| Authors: | Uri Bader Charles Frances Karin Melnick |
| Affiliation: | 1. Department of Mathematics, The Technion, 32000, Israel 2. Département de mathématiques, Université Paris-Sud, Bat. 425, 91405, Orsay Cedex, France 3. Department of Mathematics, Yale University, PO Box 208283, New Haven, CT, 06520, USA |
| 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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