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| ON NONLINEAR DIFFERENTIAL GALOIS THEORY |
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Citation： |
B. MALGRANGE.ON NONLINEAR DIFFERENTIAL GALOIS THEORY[J].Chinese Annals of Mathematics B,2002,23(2):219~226 |
| Page view： 1886
Net amount： 832 |
Authors： |
B. MALGRANGE; |
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| Abstract： |
Let X denote a complex analytic manifold, and let Aut(X) denote the space of invertible maps of a germ (X; a) to a germ (X; b); this space is obviously a groupoid; roughly speaking, a “Lie groupoid” is a subgroupoid of Aut(X) defined by a system of partial differential equations. To a foliation with singularities on X one attaches such a groupoid, e.g. the smallest one whose Lie algebra contains the vector fields tangent to the foliation. It is called “the Galois groupoid of the foliation”. Some examples are considered, for instance foliations of codimension one, and foliations defined by linear differential equations; in this last case one recuperates the usual differential Galois group. |
Keywords： |
Differential Galois group, Complex analytic manifold, Lie groupoid |
Classification： |
22E30 |
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