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

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

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 -