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

@article{Cariena2016SolvabilityOA, title={Solvability of a Lie algebra of vector fields implies their integrability by quadratures}, author={Jos{\'e} F. Cari{\~n}ena and Fernando Falceto and Janusz Grabowski}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2016}, volume={49} }

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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