Abstract
Let G be a complex algebraic group and let X = Spec R be an affine G-variety. Let φ be a G-endomorphism of X which induces an automorphism of the invariant subring R G . We show that φ is a G-automorphism when G is unipotent and X is factorial. When G is reductive, we give some conditions under which φ is a G-automorphism.
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