The Auslander conjecture for NIL-affine crystallographic groups |
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Authors: | Email author" target="_blank">Dietrich?BurdeEmail author Karel?Dekimpe Sandra?Deschamps |
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Institution: | (1) Fakultät für Mathematik, Universität Wien, Nordbergstr. 15, 1090 Wien, Austria;(2) Katholieke Universiteit Leuven, Campus Kortrijk, 8500 Kortrijk, Belgium |
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Abstract: | Let N be a simply connected, connected real nilpotent Lie group of finite dimension n. We study subgroups in Aff(N)=N Aut(N) acting properly discontinuously and cocompactly on N. This situation is a natural generalization of the so-called affine crystallographic groups. We prove that for all dimensions 1 n 5 the generalized Auslander conjecture holds, i.e., that such subgroups are virtually polycyclic. |
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