This group gathers theorems about Lie algebras and about representation theory, which studies abstract algebraic objects by letting them act on vector spaces. It covers the structure of Lie algebras and their universal enveloping algebras, the decomposition of representations of finite and compact groups into irreducible pieces, and the relations between induced and restricted representations. A theorem belongs here when its cited article places it in the theory of Lie algebras or in representation theory.
All Lie Algebras and Representation Theory
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Schur's Lemma (Representation Theory) (Wikipedia)
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In mathematics, Schur's lemma is an elementary but useful statement in representation theory of groups and algebras.
Maschke's Theorem (Wikipedia)
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named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations
Poincare-Birkhoff-Witt theorem (Wikipedia)
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In mathematics, more specifically in the theory of Lie algebras, the Poincaré-Birkhoff-Witt theorem (or PBW theorem)
Lie's theorem, Wikipedia
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In mathematics, specifically the theory of Lie algebras, Lie's theorem states that, over an algebraically
Ado's Theorem (Wikipedia)
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theorem is a theorem characterizing finite-dimensional Lie algebras.
Peter-Weyl theorem (Wikipedia)
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part states that the matrix coefficients of irreducible representations of G are dense in the space C(G) of continuous
Frobenius reciprocity, Wikipedia
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In mathematics, and in particular representation theory, Frobenius reciprocity is a theorem expressing
Weyl's theorem on complete reducibility, Wikipedia
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reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation
Lie-Kolchin theorem, Wikipedia
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In mathematics, the Lie-Kolchin theorem is a theorem in the representation theory of linear algebraic groups; Lie's theorem is
Levi decomposition, Wikipedia
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In Lie theory and representation theory, the Levi decomposition, conjectured by Wilhelm
Kostant's convexity theorem - Wikipedia
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by Bertram Kostant (1973), can be used to derive Lie-theoretical extensions of the Golden-Thompson inequality
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