On affinely closed homogeneous spaces
  Affinely closed homogeneous spaces G/H, i.e., affine homogeneous spaces that admit only the trivial affine embedding, are characterized for any affine algebraic group G. As a corollary, a description of affine G-algebras with finitely generated invariant subalgebras is obtained. 
Ivan V. Arzhantsev and Natalia A. Tennova