About: Weyl's theorem on complete reducibility

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In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation theory of semisimple Lie algebras). Let be a semisimple Lie algebra over a field of characteristic zero. The theorem states that every finite-dimensional module over is semisimple as a module (i.e., a direct sum of simple modules.)

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rdfs:label	Satz von Weyl (Lie-Algebra) (de) Weyl's theorem on complete reducibility (en)
rdfs:comment	Der Satz von Weyl, benannt nach Hermann Weyl, ist ein wichtiger Satz aus der Theorie der Lie-Algebren. Er besagt im Wesentlichen, dass man endlichdimensionale Darstellungen halbeinfacher Lie-Algebren aus irreduziblen zusammensetzen kann, sofern der Grundkörper algebraisch abgeschlossen ist und die Charakteristik 0 hat. (de) In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation theory of semisimple Lie algebras). Let be a semisimple Lie algebra over a field of characteristic zero. The theorem states that every finite-dimensional module over is semisimple as a module (i.e., a direct sum of simple modules.) (en)
name	Proposition (en)
dcterms:subject	Lie algebras
Wikipage page ID	39330817 (xsd:integer)
Wikipage revision ID	996755843 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Borel subalgebra Lie's theorem Lie algebra representation Lie group–Lie algebra correspondence Whitehead's lemma (Lie algebra) Lie algebras Maximal submodule Jordan–Chevalley decomposition Universal enveloping algebra Homological algebra Nathan Jacobson Casimir element Semisimple ring Schur's lemma Verma module Unitarian trick Semisimple representation Representation theory of semisimple Lie algebras Enveloping algebra of a representation Derivation (algebra) Chevalley generators
Link from a Wikipage to an external page	http://amathew.wordpress.com/2010/01/31/weyls-theorem-on-complete-reducibility/ https://archive.org/details/introductiontoli00jame https://books.google.com/books%3Fid=kuEjSb9teJwC&q=Victor%20G.%20Kac&pg=PP1
sameAs	Weyl's theorem on complete reducibility Weyl's theorem on complete reducibility Weyl's theorem on complete reducibility Weyl's theorem on complete reducibility Weyl's theorem on complete reducibility
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_book dbt:Clarify dbt:ISBN dbt:Reflist dbt:Math_theorem
has abstract	Der Satz von Weyl, benannt nach Hermann Weyl, ist ein wichtiger Satz aus der Theorie der Lie-Algebren. Er besagt im Wesentlichen, dass man endlichdimensionale Darstellungen halbeinfacher Lie-Algebren aus irreduziblen zusammensetzen kann, sofern der Grundkörper algebraisch abgeschlossen ist und die Charakteristik 0 hat. (de) In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation theory of semisimple Lie algebras). Let be a semisimple Lie algebra over a field of characteristic zero. The theorem states that every finite-dimensional module over is semisimple as a module (i.e., a direct sum of simple modules.) (en)
math statement	Let be a semisimple finite-dimensional Lie algebra over a field of characteristic zero. # There exists a unique pair of elements in such that , is semisimple, is nilpotent and . # If is a finite-dimensional representation, then and , where denote the Jordan decomposition of the semisimple and nilpotent parts of the endomorphism . In short, the semisimple and nilpotent parts of an element of are well-defined and are determined independent of a faithful finite-dimensional representation. (en)
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page length (characters) of wiki page	14711 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Weyl's_theorem_on_complete_reducibility
is Link from a Wikipage to another Wikipage of	Representation theory Semi-simplicity Representation of a Lie group Lie algebra cohomology Lie algebra representation Whitehead's lemma (Lie algebra) Lie algebra Haboush's theorem Weyl's theorem Casimir element List of things named after Hermann Weyl Semisimple Lie algebra Semisimple representation Representation theory of semisimple Lie algebras Weyl's complete reducibility theorem Weyl's completely reducibility theorem
is Wikipage redirect of	Weyl's complete reducibility theorem Weyl's completely reducibility theorem
is Wikipage disambiguates of	Weyl's theorem
is foaf:primaryTopic of	wikipedia-en:Weyl's_theorem_on_complete_reducibility

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