English

Cartan projections of some non-reductive subgroups and proper actions on homogeneous spaces

Differential Geometry 2022-06-13 v2 Group Theory Geometric Topology Representation Theory

Abstract

Kobayashi [Duke Math. J. (1992)] gave a necessary condition for the existence of compact Clifford-Klein forms in terms of Cartan projections and non-compact dimensions of reductive subgroups. We extend his method to non-reductive subgroups, and give some examples of homogeneous spaces of reductive type that do not admit compact Clifford-Klein forms by comparing Cartan projections and non-compact dimensions of reductive subgroups with those of non-reductive subgroups.

Keywords

Cite

@article{arxiv.2106.07848,
  title  = {Cartan projections of some non-reductive subgroups and proper actions on homogeneous spaces},
  author = {Yosuke Morita},
  journal= {arXiv preprint arXiv:2106.07848},
  year   = {2022}
}

Comments

22 pages, presentation improved, Sections 6 and 7 merged into a single section, to appear in Transform. Groups