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Solvability of a Lie algebra of vector fields implies their integrability by quadratures

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arxiv 1606.02472 v2 pith:EGXW2UOZ submitted 2016-06-08 math-ph math.MP

J.F. Cariñena , F. Falceto , J. Grabowski This is my paper · ORCID
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keywords fieldsquadraturesvectoralgebraintegrabilityclassicalfinite-dimensionalgeneralisation
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We present a substantial generalisation of a classical result by Lie on integrability by quadratures. Namely, we prove that all vector fields in a finite-dimensional transitive and solvable Lie algebra of vector fields on a manifold can be integrated by quadratures.

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  1. Contact line bundles, foliations, and integrability

    math.SG 2025-02 conditional novelty 6.0 of 10

    A line-bundle approach to contact integrability unifies cooriented and non-cooriented systems and covers dissipative contact Hamiltonians.

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