On the envelope of a vector field

Bernard Malgrange

On the envelope of a vector field

Bernard Malgrange

Banach Center Publications (2011)

Volume: 94, Issue: 1, page 239-246
ISSN: 0137-6934

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Abstract

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Given a vector field X on an algebraic variety V over ℂ, I compare the following two objects: (i) the envelope of X, the smallest algebraic pseudogroup over V whose Lie algebra contains X, and (ii) the Galois pseudogroup of the foliation defined by the vector field X + d/dt (restricted to one fibre t = constant). I show that either they are equal, or the second has codimension one in the first.

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Bernard Malgrange. "On the envelope of a vector field." Banach Center Publications 94.1 (2011): 239-246. <http://eudml.org/doc/282371>.

@article{BernardMalgrange2011,
abstract = {Given a vector field X on an algebraic variety V over ℂ, I compare the following two objects: (i) the envelope of X, the smallest algebraic pseudogroup over V whose Lie algebra contains X, and (ii) the Galois pseudogroup of the foliation defined by the vector field X + d/dt (restricted to one fibre t = constant). I show that either they are equal, or the second has codimension one in the first.},
author = {Bernard Malgrange},
journal = {Banach Center Publications},
keywords = {vector fields; differential Galois theory},
language = {eng},
number = {1},
pages = {239-246},
title = {On the envelope of a vector field},
url = {http://eudml.org/doc/282371},
volume = {94},
year = {2011},
}

TY - JOUR
AU - Bernard Malgrange
TI - On the envelope of a vector field
JO - Banach Center Publications
PY - 2011
VL - 94
IS - 1
SP - 239
EP - 246
AB - Given a vector field X on an algebraic variety V over ℂ, I compare the following two objects: (i) the envelope of X, the smallest algebraic pseudogroup over V whose Lie algebra contains X, and (ii) the Galois pseudogroup of the foliation defined by the vector field X + d/dt (restricted to one fibre t = constant). I show that either they are equal, or the second has codimension one in the first.
LA - eng
KW - vector fields; differential Galois theory
UR - http://eudml.org/doc/282371
ER -

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