English

Proper affine actions on semisimple Lie algebras

Group Theory 2016-05-13 v2

Abstract

For any noncompact semisimple real Lie group GG, we construct a group of affine transformations of its Lie algebra g\mathfrak{g} whose linear part is Zariski-dense in AdG\operatorname{Ad} G and which is free, nonabelian and acts properly discontinuously on g\mathfrak{g}.

Keywords

Cite

@article{arxiv.1406.5906,
  title  = {Proper affine actions on semisimple Lie algebras},
  author = {Ilia Smilga},
  journal= {arXiv preprint arXiv:1406.5906},
  year   = {2016}
}

Comments

Section 3 of this paper draws heavily on the section 3 from my earlier paper arXiv:1303.3766 This is the version that appeared in Geometriae Dedicata. I have corrected some mistakes, added a few examples and added a proof that the Margulis invariant is well-defined