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Journal of Lie Theory 11 (2001), No. 1, 111--128
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 finite-dimensional 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.

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