| dbo: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) |
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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 |
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| dbp:mathStatement |
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) |
| dbp:name |
Proposition (en) |
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dbc:Lie_algebras |
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| 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) |
| rdfs:label |
Satz von Weyl (Lie-Algebra) (de) Weyl's theorem on complete reducibility (en) |
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