Superrigidity of lattices in solvable Lie groups |
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Authors: | Dave Witte |
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Institution: | (1) Department of Mathematics, Williams College, 01267 Williamstown, MA, USA;(2) Present address: Department of Mathematics, Oklahoma State University, 74078 Stillwater, OK, USA |
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Abstract: | Summary Let be a closed, cocompact subgroup of a simply connected, solvable Lie groupG, such that Ad
G
has the same Zariski closure as AdG. If : GL
n
() is any finite-dimensional representation of , we show that virtually extends to a representation ofG. (By combining this with work of Margulis on lattices in semisimple groups, we obtain a similar result for lattices in many groups that are neither solvable nor semisimple.) Furthermore, we show that if is isomorphic to a closed, cocompact subgroup of another simply connected, solvable Lie groupG, then any isomorphism from to extends to a crossed isomorphism fromG toG. In the same vein, we prove a more concrete form of Mostow's theorem that compact solvmanifolds with isomorphic fundamental groups are diffeomorphic.Oblatum 5-VII-1994 & 15-IV-1995 |
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Keywords: | |
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