Refines the Lie-Amaldi classification of finite dimensional nilpotent algebras of vector fields using the rank of the center of the Lie algebra as an invariant.
Three-dimensional homogeneous spaces with non-solvable transformation groups
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abstract
We classify all transitive actions of Lie algebras of vector fields on C^3 and R^3 up to a local equivalence and discuss why this classification can not be extended in general to the solvable case. The main technical tool is the structure of one-dimensional invariant foliations on homogeneous spaces.
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A Note On The Lie-Amaldi Classification
Refines the Lie-Amaldi classification of finite dimensional nilpotent algebras of vector fields using the rank of the center of the Lie algebra as an invariant.