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Levi decomposition

In Lie theory and representation theory, the Levi decomposition, conjectured by Wilhelm Killing and Élie Cartan and proved by Eugenio Elia Levi (1905), states that any finite-dimensional Lie algebra g over a field of characteristic zero is the semidirect product of a solvable ideal and a semisimple subalgebra. One is its radical, a maximal solvable…

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Conjectured by
Wilhelm Killing Élie Cartan
Conjectured in
1888
Field
Representation theory
First proof by
Eugenio Elia Levi
First proof in
1905

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Levi decomposition

Nodes35
Edges34
Triples11
Avg. degree1.94
Density0.057143
Components1

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Levi decomposition

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related to Extensions of the results · 6
Levi decomposition → Analogous, George Mostow, In, Levi, Lie, The Langlands
Conjectured by · 1
Levi decomposition → Wilhelm Killing Élie Cartan
Conjectured in · 1
Levi decomposition → 1888
Field · 1
Levi decomposition → Representation theory
First proof by · 1
Levi decomposition → Eugenio Elia Levi
First proof in · 1
Levi decomposition → 1905

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Important terminology

levi lie semisimple decomposition algebras solvable algebra called representation finite-dimensional subalgebra characteristic also theory eugenio field radical ideal two theorem

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SubjectPredicateObjectConfidenceSrc
Levi decompositionConjectured byWilhelm Killing Élie Cartan1.00infobox
Levi decompositionConjectured in18881.00infobox
Levi decompositionFieldRepresentation theory1.00infobox
Levi decompositionFirst proof byEugenio Elia Levi1.00infobox
Levi decompositionFirst proof in19051.00infobox
Levi decompositionrelated to Extensions of the resultsIn0.60section
Levi decompositionrelated to Extensions of the resultsLevi0.60section
Levi decompositionrelated to Extensions of the resultsThe Langlands0.60section
Levi decompositionrelated to Extensions of the resultsAnalogous0.60section
Levi decompositionrelated to Extensions of the resultsLie0.60section
Levi decompositionrelated to Extensions of the resultsGeorge Mostow0.60section

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