Clifford-Klein form

Clifford-Klein form

In mathematics, a Clifford-Klein form is a double coset space

:Γ/"G""H",

where "G" is a reductive Lie group, "H" a closed subgroup of "G", and Γ a discrete subgroup of G that acts properly discontinuously on the homogeneous space "G""H". A suitable discrete subgroup Γ may or may not exist, for a given "G" and "H". If Γ exists, there is the question of whether Γ/"G""H" can be taken to be a compact space, called a compact Clifford-Klein form.

When "H" is itself compact, classical results show that a compact Clifford-Klein form exists. Otherwise it may not, and there are a number of negative results.


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