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

Abstract

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.

14 pages. Published version

References in corpus (1)

• Geometry of Lie integrability by quadratures

Cited by in corpus (5)

• Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations
• Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems
• Integrable systems in cosymplectic geometry
• Quasi-Lie schemes for PDEs
• Contact line bundles, foliations, and integrability