Resumen de Automorphismes de certains complétés du corps de Weyl quantique
Let $k$ be a field and $\sigma$ the $k$-automorphism of $k((Y ))$ defined by: $\sigma(Y) = qY$, with $q\in k^\ast$. The purpose of this article is the description of the group Aut$_k(Lq)$ for the extension $Lq = k((Y ))((X;\sigma))$ of the quantum Weyl skewfield $D^q_1 = k(Y )(X;\sigma)$, when $q$ is not a root of one. The motivations of the main theorem (theorem 2.7) are detailed in the first part of the paper, devoted to the two-dimensional quantum Cremona transformations. Its proof is based on a general result (theorem 2.3) concerning the continuity of automorphisms in Laurent series skewfields, which also holds in the classical case (remark 2.10).
