Dérivations, et hautes dérivations, dans certains corps gauches de series de Laurent

François Dumas and Robert Vidal

Vol. 153 (1992), No. 2, 277–288

DOI: 10.2140/pjm.1992.153.277

Abstract

Let k be a field of characteristic zero, F = k((Y )) the local field of Laurent series in a variable Y , and ∂_Y the usual derivation of F. The purpose of this paper is the complete description of k-derivations on the formal pseudo-differential operator skewfield K = F((X,∂_Y )). An application of this result is given to study the structure of higher derivations in skewfields of characteristic zero.

Mathematical Subject Classification 2000

Primary: 16W25

Secondary: 16K99, 16W60

Milestones

Received: 12 October 1990

Revised: 13 March 1991

Published: 1 April 1992