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 Lie's conjecture for such Lie algebras. Also, infinite-dimensional analytically solvable and transitive Lie algebras of vector fields whose derivative ideal is nilpotent can be adapted to this scheme.