Complete constructive classification of nilpotent Lie algebras of vector fields in three variables, organized by rank and dimension of the center as the key 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.
fields
math.RT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Outlines brief proofs of Lie's classification for finite dimensional vector field subalgebras in low dimensions and maximal rank algebras in C^N for arbitrary N.
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