Lie's Theorem states that every finite-dimensional representation of a solvable Lie algebra over an algebraically closed field of characteristic zero can be put in upper-triangular form by a suitable choice of basis. Named for Sophus Lie, it is a foundational structural result of Lie algebra representation theory, playing a role for solvable Lie algebras analogous to triangularization results for solvable groups.
Facts
StatementOver an algebraically closed field of characteristic zero, every finite-dimensional representation of a solvable Lie algebra has a flag of invariant subspaces, so it can be put in upper-triangular form. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Source Lie's theorem, Wikipedia
Sources
1. Lie's theorem, Wikipedia
Lead paragraphQuote, Lead paragraph
In mathematics, specifically the theory of Lie algebras, Lie's theorem states that, over an algebraically closed field of characteristic zero,
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