Abstract
We calculate the invariant subspaces in the linear representation of the group of algebraic automorphisms of ℂnon the vector space of algebraic vector fields on ℂnand more generally we do this in a setting with parameter. As an application to the field of Several Complex Variables we get a new proof of the Andersén–Lempert observation and a parametric version of the Andersén–Lempert theorem. Further applications to the question of embeddings of ℂkinto ℂnare announced.
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