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Unitarian Trick
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Geliefert zwischen Do., 29.01.2026 und Fr., 30.01.2026
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High Quality Content by WIKIPEDIA articles! In mathematics, the unitarian trick (occasionally unitariantrick [sic]) is a device in the representation theory of Lie groups, introduced by Hermann Weyl. It applies to show that the representation theory of some group G is in a qualitative way controlled by that of some other compact group K. An important example is that in which G is the complex general linear group, and K the unitary group acting on vectors of the same size. From the fact that the representations of K are completely reducible, the same is concluded for those of G, at least in finite dimensions. The relationship between G and K that drives this connection is traditionally expressed in the terms that the Lie algebra of K is a real form of that of G. In the theory of algebraic groups, the relationship can also be put that K is a dense subset of G, for the Zariski topology. The trick works for reductive Lie groups (suitably defined), of which an important case are semisimple Lie groups.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131116155
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131116155
- Format Fachbuch
- Titel Unitarian Trick
- Herausgeber Betascript Publishing
- Anzahl Seiten 72
- Genre Mathematik
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