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