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arXiv · 1409.7549

Geometry of Lie integrability by quadratures

J. F. Cariñena·F. Falceto·J. Grabowski·M. F. Rañada
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Abstract

In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way. It turns out that the conditions can be expressed in a purely algebraic way. In a second step we generalize the construction to the case in which we substitute the Lie algebra of vector fields by a module (generalized distribution). We obtain much larger class of integrable systems replacing standard concepts of solvable (or nilpotent) Lie algebra with distributional solvability (nilpotency).

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BibTeXRIS

J. F. Cariñena, F. Falceto, J. Grabowski, M. F. Rañada. 2014-09-26. Geometry of Lie integrability by quadratures. https://doi.org/10.1088/1751-8113/48/21/215206

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