caa a22 4500 445884010 CHVBK 20180317145553.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s10711-010-9554-z doi (NATIONALLICENCE)springer-10.1007/s10711-010-9554-z The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant [Elektronische Daten] [H. Abels, G. Margulis, G. Soifer] In this paper we study the dynamics of properly discontinuous and crystallographic affine groups leaving a quadratic from of signature (p, q) invariant. The main results are: (I) If p − q ≥ 2, then the linear part of the group is not Zariski dense in the corresponding orthogonal group. (II) If q = 2 and the group is crystallographic, then the group is virtually solvable. This proves the Auslander conjecture for this case. Springer Science+Business Media B.V., 2010 Affine group nationallicence Crystallographic group nationallicence Virtually solvable group nationallicence Abels H. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany aut Margulis G. Department of Mathematics, Yale University, 06520, New Haven, CT, USA aut Soifer G. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel aut Geometriae Dedicata Springer Netherlands 153/1(2011-08-01), 1-46 0046-5755 153:1<1 2011 153 10711 https://doi.org/10.1007/s10711-010-9554-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9554-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Abels H. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany aut NATIONALLICENCE 700 1- Margulis G. Department of Mathematics, Yale University, 06520, New Haven, CT, USA aut NATIONALLICENCE 700 1- Soifer G. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 153/1(2011-08-01), 1-46 0046-5755 153:1<1 2011 153 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer