
Journal of Lie Theory 11 (2001), No. 1, 111128 Copyright Heldermann Verlag 2001 On the Structure of Transitively Differential Algebras Gerhard Post Faculty of Mathematical Sciences, University of Twente, 7500 AE Enschede, The Netherlands We study finitedimensional Lie algebras of polynomial vector fields in n variables that contain all partial derivatives and the Euler operator. We derive some general results on the structure of such Lie algebras, and provide the complete classification in the cases n=2 and n=3. Finally we describe a certain construction in high dimensions. [ Fulltextpdf (217 KB)] 