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Solvable Lie algebras of vector fields and a Lie’s conjecture. (English) Zbl 07227210
Summary: 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.

##### MSC:
 17B30 Solvable, nilpotent (super)algebras 17B66 Lie algebras of vector fields and related (super) algebras 57R25 Vector fields, frame fields in differential topology 57S20 Noncompact Lie groups of transformations
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##### References:
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