Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 7 (2007) no. 4, pp. 74-88
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M. V. Neshchadim. The Lie commutators on the space of the smooth functions from $R^1$ to $R^2$. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 7 (2007) no. 4, pp. 74-88. http://geodesic.mathdoc.fr/item/VNGU_2007_7_4_a4/
@article{VNGU_2007_7_4_a4,
author = {M. V. Neshchadim},
title = {The {Lie} commutators on the space of the smooth functions from $R^1$ to $R^2$},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {74--88},
year = {2007},
volume = {7},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2007_7_4_a4/}
}
TY - JOUR
AU - M. V. Neshchadim
TI - The Lie commutators on the space of the smooth functions from $R^1$ to $R^2$
JO - Sibirskij žurnal čistoj i prikladnoj matematiki
PY - 2007
SP - 74
EP - 88
VL - 7
IS - 4
UR - http://geodesic.mathdoc.fr/item/VNGU_2007_7_4_a4/
LA - ru
ID - VNGU_2007_7_4_a4
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%A M. V. Neshchadim
%T The Lie commutators on the space of the smooth functions from $R^1$ to $R^2$
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2007
%P 74-88
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%U http://geodesic.mathdoc.fr/item/VNGU_2007_7_4_a4/
%G ru
%F VNGU_2007_7_4_a4
In this paper we consider the classification problem of the local algebras Lie on the space $C^\infty(R^n,R^m)$. For $n=1$, $m=2$ and the symmetry analytical Lie commutators of the first order we obtain full classification under the module of the action of the group $GL_2(F)$, where $F$ is the space analytical functions from one variable.
