Abstract

Let be a purely transcendental extension of the field kof transcendence degree d. A k-automorphism of K is said to be affine (resp. linear) if it acts on the k-subspace of K generated by . In this article, we give a simple canonical form for affine automorphisms (modulo linear ones) and we extend to affine automorphisms (a stronger form of) the negligibility theorem proved for linear ones in [3,Theorem 1.5], We also discuss the question of how much of an affine automorphism (of finite order) is determined by its order and we show that in certain cases an affine automorphism is completely characterized by its order.

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