About: Lie's third theorem

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In the mathematics of Lie theory, Lie's third theorem states that every finite-dimensional Lie algebra over the real numbers is associated to a Lie group . The theorem is part of the Lie group–Lie algebra correspondence.

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rdfs:label	Tercer teorema de Lie (ca) Liesche Sätze (de) Lie's third theorem (en) Lies tredje sats (sv)
rdfs:comment	In der Mathematik stellen die Lie’schen Sätze, benannt nach Sophus Lie, den Zusammenhang zwischen Lie-Gruppen und Lie-Algebren her. (de) Inom matematiken är Lies tredje sats en sats som säger att en ändligdimensionell Liealgebra g över de reella talen är associerad till en Liegrupp G. Satsen är uppkallad efter Sophus Lie. (sv) En matemàtiques, i més concretament en la , el tercer teorema de Lie (pronunciat /liː/) afirma que tota àlgebra de Lie de dimensió finita sobre els nombre reals té associat un grup de Lie G. El teorema forma part de la . (ca) In the mathematics of Lie theory, Lie's third theorem states that every finite-dimensional Lie algebra over the real numbers is associated to a Lie group . The theorem is part of the Lie group–Lie algebra correspondence. (en)
dcterms:subject	Lie algebras Theorems about algebras Lie groups
Wikipage page ID	10875756 (xsd:integer)
Wikipage revision ID	1111023020 (xsd:integer)
Link from a Wikipage to another Wikipage	Vector field Infinitesimal transformation Jacobi identity Lie algebroid Lie group Lie group action Lie group integrator Lie groupoid Lie group–Lie algebra correspondence Lie theory Lie algebras Mathematical induction Mathematics Matrix (mathematics) Matrix exponential Maurer–Cartan form Constructive proof Equivalence of categories Lie algebra Élie Cartan Path (topology) Banach space Ado's theorem Theorems about algebras American Mathematical Society Lie groups Graduate Studies in Mathematics Simply connected space Group action (mathematics) Hans Duistermaat Jean-Pierre Serre Chevalley-Eilenberg complex Sophus Lie Category (mathematics) Smooth manifold Center of a Lie algebra Local Lie group
Link from a Wikipage to an external page	https://encyclopediaofmath.org/wiki/Lie_theorem
sameAs	Lie's third theorem Lie's third theorem Lie's third theorem Lie's third theorem Lie's third theorem Lie's third theorem Lie's third theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Interlanguage_link dbt:Reflist dbt:Manifolds
has abstract	En matemàtiques, i més concretament en la , el tercer teorema de Lie (pronunciat /liː/) afirma que tota àlgebra de Lie de dimensió finita sobre els nombre reals té associat un grup de Lie G. El teorema forma part de la . Històricament, el terme tercer teorema de Lie feia referència a resultats diferents però relacionats. Els dos anteriors teoremes de Sophus Lie, reformulats en llenguatge matemàtic modern, relacionen les d'una acció de grup en una varietat diferenciable. El tercer teorema de la llista afirmava la identitat de Jacobi per a les transformacions infinitesimals d'un . Contràriament, en la presència d'una àlgebra de Lie de camps vectorials, la integració dona una local. El resultat, avui en dia conegut com tercer teorema, proporciona un contrari intrínsic i global al teorema original. (ca) In der Mathematik stellen die Lie’schen Sätze, benannt nach Sophus Lie, den Zusammenhang zwischen Lie-Gruppen und Lie-Algebren her. (de) In the mathematics of Lie theory, Lie's third theorem states that every finite-dimensional Lie algebra over the real numbers is associated to a Lie group . The theorem is part of the Lie group–Lie algebra correspondence. Historically, the third theorem referred to a different but related result. The two preceding theorems of Sophus Lie, restated in modern language, relate to the infinitesimal transformations of a group action on a smooth manifold. The third theorem on the list stated the Jacobi identity for the infinitesimal transformations of a local Lie group. Conversely, in the presence of a Lie algebra of vector fields, integration gives a local Lie group action. The result now known as the third theorem provides an intrinsic and global converse to the original theorem. (en) Inom matematiken är Lies tredje sats en sats som säger att en ändligdimensionell Liealgebra g över de reella talen är associerad till en Liegrupp G. Satsen är uppkallad efter Sophus Lie. (sv)
prov:wasDerivedFrom	wikipedia-en:Lie's_third_theorem?oldid=1111023020&ns=0
page length (characters) of wiki page	6475 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Lie's_third_theorem
is Link from a Wikipage to another Wikipage of	Lie algebra bundle Lie group Lie groupoid Lie group–Lie algebra correspondence Lie theory Pseudogroup Giacinto Morera Lie algebra Lie algebra extension Adjoint representation List of Lie groups topics Hans Duistermaat

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