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- Ado's_theorem abstract "In abstract algebra, Ado's theorem states that every finite-dimensional Lie algebra L over a field K of characteristic zero can be viewed as a Lie algebra of square matrices under the commutator bracket. More precisely, the theorem states that L has a linear representation ρ over K, on a finite-dimensional vector space V, that is a faithful representation, making L isomorphic to a subalgebra of the endomorphisms of V.While for the Lie algebras associated to classical groups there is nothing new in this, the general case is a deeper result. Applied to the real Lie algebra of a Lie group G, it does not imply that G has a faithful linear representation (which is not true in general), but rather that G always has a linear representation that is a local isomorphism with a linear group. It was proved in 1935 by Igor Dmitrievich Ado of Kazan State University, a student of Nikolai Chebotaryov.The restriction on the characteristic was removed later, by Iwasawa and Harish-Chandra (see also the below Gerhard Hochschild paper for a proof).".
- Ado's_theorem wikiPageExternalLink p159.
- Ado's_theorem wikiPageExternalLink home.html.
- Ado's_theorem wikiPageID "3422249".
- Ado's_theorem wikiPageRevisionID "541780691".
- Ado's_theorem hasPhotoCollection Ado's_theorem.
- Ado's_theorem subject Category:Lie_algebras.
- Ado's_theorem subject Category:Theorems_in_abstract_algebra.
- Ado's_theorem type Abstraction100002137.
- Ado's_theorem type Algebra106012726.
- Ado's_theorem type Cognition100023271.
- Ado's_theorem type Communication100033020.
- Ado's_theorem type Content105809192.
- Ado's_theorem type Discipline105996646.
- Ado's_theorem type KnowledgeDomain105999266.
- Ado's_theorem type LieAlgebras.
- Ado's_theorem type Mathematics106000644.
- Ado's_theorem type Message106598915.
- Ado's_theorem type Proposition106750804.
- Ado's_theorem type PsychologicalFeature100023100.
- Ado's_theorem type PureMathematics106003682.
- Ado's_theorem type Science105999797.
- Ado's_theorem type Statement106722453.
- Ado's_theorem type Theorem106752293.
- Ado's_theorem type TheoremsInAbstractAlgebra.
- Ado's_theorem comment "In abstract algebra, Ado's theorem states that every finite-dimensional Lie algebra L over a field K of characteristic zero can be viewed as a Lie algebra of square matrices under the commutator bracket.".
- Ado's_theorem label "Ado's theorem".
- Ado's_theorem label "Ado定理".
- Ado's_theorem label "Théorème d'Ado".
- Ado's_theorem sameAs Théorème_d'Ado.
- Ado's_theorem sameAs m.09bnvb.
- Ado's_theorem sameAs Q2028341.
- Ado's_theorem sameAs Q2028341.
- Ado's_theorem sameAs Ado's_theorem.
- Ado's_theorem wasDerivedFrom Ado's_theorem?oldid=541780691.
- Ado's_theorem isPrimaryTopicOf Ado's_theorem.