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- 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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- 14711 (xsd:nonNegativeInteger)
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- 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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- 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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- Satz von Weyl (Lie-Algebra) (de)
- Weyl's theorem on complete reducibility (en)
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