The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant

Abels H, Margulis GA, Soifer GA (2011)
Geometriae Dedicata 153(1): 1-46.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Abels, HerbertUniBi; Margulis, G. A.; Soifer, G. A.
Abstract / Bemerkung
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 a parts per thousand yen 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.
Stichworte
Virtually solvable group; Affine group; Crystallographic group
Erscheinungsjahr
2011
Zeitschriftentitel
Geometriae Dedicata
Band
153
Ausgabe
1
Seite(n)
1-46
ISSN
0046-5755
Page URI
https://pub.uni-bielefeld.de/record/2307070

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Abels H, Margulis GA, Soifer GA. The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant. Geometriae Dedicata. 2011;153(1):1-46.
Abels, H., Margulis, G. A., & Soifer, G. A. (2011). The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant. Geometriae Dedicata, 153(1), 1-46. doi:10.1007/s10711-010-9554-z
Abels, H., Margulis, G. A., and Soifer, G. A. (2011). The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant. Geometriae Dedicata 153, 1-46.
Abels, H., Margulis, G.A., & Soifer, G.A., 2011. The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant. Geometriae Dedicata, 153(1), p 1-46.
H. Abels, G.A. Margulis, and G.A. Soifer, “The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant”, Geometriae Dedicata, vol. 153, 2011, pp. 1-46.
Abels, H., Margulis, G.A., Soifer, G.A.: The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant. Geometriae Dedicata. 153, 1-46 (2011).
Abels, Herbert, Margulis, G. A., and Soifer, G. A. “The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant”. Geometriae Dedicata 153.1 (2011): 1-46.