Abstract
We define a closed subgroup H of a pro–affine algebraic group G to be observable if every (finite dimensional) rational H module is an H submodule of a rational G module. We show the equivalence to observability of a number of other conditions on the pair G,H, including the condition that the provariety G/H be pro–quasi–affine. To treat this latter, we also include results on the foundations of provarieties.
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