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An additive action on an irreducible algebraic variety X is an effective action 
with an open orbit of the vector group 
. Any two additive actions on X are conjugate by a birational automorphism of X. We prove that, if X is the projective space, the conjugating element can be chosen in the affine Cremona group and it is given by so-called basic polynomials of the corresponding local algebra.
Mathematics Subject Classification (2020):
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