Solvable Lie Algebras of Vector Fields and a Lie's Conjecture

Abstract

We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional analytical solvable and transitive Lie algebras of vector fields whose derivative ideal is nilpotent can be adapted to this scheme.

References in corpus (4)

• $Q$-manifolds and Higher Analogs of Lie Algebroids
• Linear duals of graded bundles and higher analogues of (Lie) algebroids
• Geometry of Lie integrability by quadratures
• Projectable Lie algebras of vector fields in 3D

Cited by in corpus (3)

• Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems
• The neighbourhood of a singular leaf
• Transitive nilpotent Lie algebras of vector fields and their Tanaka prolongations