Lie's theorem
id:
lie-s-theorem-292-18047597
title:
Lie's theorem
text:
In mathematics, specifically the theory of Lie algebras, Lie's theorem states that, over an algebraically closed field of characteristic zero, if π : g → g l :{\mathfrak {g}}\to {\mathfrak {gl}}(V)} is a finite-dimensional representation of a solvable Lie algebra, then there's a flag V = V 0 ⊃ V 1 ⊃ ⋯ ⊃ V n = 0 of invariant subspaces of π with codim V i = i , meaning that π ⊆ V i for each X ∈ g and i. Put in another way, the theorem says there is a basis for V such that all linear transformat
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https://en.wikipedia.org/wiki/Lie%27s_theorem
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date modified:
2023-11-04T12:02:40Z
main entity:
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