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.
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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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1. Lie's theorem, Wikipedia
Lead paragraph
In mathematics, specifically the theory of Lie algebras, Lie's theorem states that, over an algebraically closed field of characteristic zero,
In Group: Lie Algebras and Representation Theory, Lead section
In mathematics, specifically the theory of Lie algebras, Lie's theorem states that, over an algebraically
In Branch: Lie Theory, Lead section
In mathematics, specifically the theory of Lie algebras, Lie's theorem states that, over an algebraically
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