Group Analysis of Differential Equations and Integrable Systems − 2018

Janusz Grabowski (Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland)

On a Lie's theorem about integrability by quadratures

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.

[1] Cariñena, J. F.; Falceto, F.; Grabowski, J. Solvability of a Lie algebra of vector fields implies their integrability by quadratures. J. Phys. A 49 (2016), no. 42, 425202, 13 pp.