TY - JOUR
T1 - On the zariski closure of the linear part of a properly discontinuous group of affine transformations
AU - Abels, H.
AU - Margulis, G. A.
AU - Soifer, G. A.
PY - 2002
Y1 - 2002
N2 - Let Γ be a subgroup of the group of affine transformations of the affine space ℝ2n+1. Suppose Γ acts properly discontinuously on ℝ2n+1. The paper deals with the question which subgroups of GL(2n+1,ℝ) occur as Zariski closure ℓ(Γ)¯ of the linear part of such a group Γ. The two main results of the paper say that SO(n + 1, n) does occur as ℓ(Γ)¯ of such a group Γ if n is odd, but does not if n is even.
AB - Let Γ be a subgroup of the group of affine transformations of the affine space ℝ2n+1. Suppose Γ acts properly discontinuously on ℝ2n+1. The paper deals with the question which subgroups of GL(2n+1,ℝ) occur as Zariski closure ℓ(Γ)¯ of the linear part of such a group Γ. The two main results of the paper say that SO(n + 1, n) does occur as ℓ(Γ)¯ of such a group Γ if n is odd, but does not if n is even.
UR - http://www.scopus.com/inward/record.url?scp=1642468031&partnerID=8YFLogxK
U2 - 10.4310/jdg/1090351104
DO - 10.4310/jdg/1090351104
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AN - SCOPUS:1642468031
SN - 0022-040X
VL - 60
SP - 315
EP - 344
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
IS - 2
ER -