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

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.

arXiv comment22 pages, presentation improved, Sections 6 and 7 merged into a single section, to appear in Transform. Groups

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