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- Levi_decomposition abstract "In Lie theory and representation theory, the Levi decomposition, conjectured by Killing and Cartan and proved by Eugenio Elia Levi (1905), states that any finite-dimensional real Lie algebra g is the semidirect product of a solvable ideal and a semisimple subalgebra.One is its radical, a maximal solvable ideal, and the other is a semisimple subalgebra, called a Levi subalgebra. Levi decomposition implies that any finite-dimensional Lie algebra is a semidirect product of a solvable Lie algebra and a semisimple Lie algebra.When viewed as a factor-algebra of g, this semisimple Lie algebra is also called the Levi factor of g.Moreover, Malcev (1942) showed that any two Levi subalgebras are conjugate by an (inner) automorphism of the formwhere z is in the nilradical (Levi–Malcev theorem).".
- Levi_decomposition wikiPageExternalLink attidellarealeac40real.
- Levi_decomposition wikiPageExternalLink 2up.
- Levi_decomposition wikiPageID "2774198".
- Levi_decomposition wikiPageRevisionID "604695072".
- Levi_decomposition author "A.I. Shtern".
- Levi_decomposition authorlink "Eugenio Elia Levi".
- Levi_decomposition first "Eugenio Elia".
- Levi_decomposition hasPhotoCollection Levi_decomposition.
- Levi_decomposition id "Levi%E2%80%93Mal%27tsev_decomposition".
- Levi_decomposition last "Levi".
- Levi_decomposition title "Levi-Mal'tsev decomposition".
- Levi_decomposition year "1905".
- Levi_decomposition subject Category:Lie_algebras.
- Levi_decomposition type Abstraction100002137.
- Levi_decomposition type Algebra106012726.
- Levi_decomposition type Cognition100023271.
- Levi_decomposition type Content105809192.
- Levi_decomposition type Discipline105996646.
- Levi_decomposition type KnowledgeDomain105999266.
- Levi_decomposition type LieAlgebras.
- Levi_decomposition type Mathematics106000644.
- Levi_decomposition type PsychologicalFeature100023100.
- Levi_decomposition type PureMathematics106003682.
- Levi_decomposition type Science105999797.
- Levi_decomposition comment "In Lie theory and representation theory, the Levi decomposition, conjectured by Killing and Cartan and proved by Eugenio Elia Levi (1905), states that any finite-dimensional real Lie algebra g is the semidirect product of a solvable ideal and a semisimple subalgebra.One is its radical, a maximal solvable ideal, and the other is a semisimple subalgebra, called a Levi subalgebra.".
- Levi_decomposition label "Levi decomposition".
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- Levi_decomposition sameAs Q6535568.
- Levi_decomposition sameAs Q6535568.
- Levi_decomposition sameAs Levi_decomposition.
- Levi_decomposition wasDerivedFrom Levi_decomposition?oldid=604695072.
- Levi_decomposition isPrimaryTopicOf Levi_decomposition.