1Faculty of Mathematical Sciences, University of Twente, 7500 AE Enschede, The Netherlands 2We 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. 3[
Journal of Lie Theory, Tome 11 (2001) no. 1, pp. 111-128
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Gerhard Post. On the Structure of Transitively Differential Algebras. Journal of Lie Theory, Tome 11 (2001) no. 1, pp. 111-128. http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a5/
@article{JOLT_2001_11_1_a5,
author = {Gerhard Post},
title = {On the {Structure} of {Transitively} {Differential} {Algebras}},
journal = {Journal of Lie Theory},
pages = {111--128},
year = {2001},
volume = {11},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a5/}
}
TY - JOUR
AU - Gerhard Post
TI - On the Structure of Transitively Differential Algebras
JO - Journal of Lie Theory
PY - 2001
SP - 111
EP - 128
VL - 11
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a5/
ID - JOLT_2001_11_1_a5
ER -
%0 Journal Article
%A Gerhard Post
%T On the Structure of Transitively Differential Algebras
%J Journal of Lie Theory
%D 2001
%P 111-128
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a5/
%F JOLT_2001_11_1_a5
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.
