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Representation Reguliere

Формат:      Страниц 80
     мягкая обложка
Frederic P.    
Книга по Требованию    
1395 руб
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En mathematiques et plus precisement en theorie des groupes, la representation reguliere est une representation d' un groupe fini. Soient G un groupe fini d' ordre g, K un corps, V un K espace vectoriel de dimension g et (es) une base de V indexee par G. Soit ? le morphisme de groupe de G dans le groupe lineaire GL(V), qui a un element u de G associe l' automorphisme ? u de V defini comme suit sur la base de V : l' image du vecteur es par ? u est egal au vecteur eu. s. Alors la representation (V, ? ) est appelee representation reguliere de G. Ce concept possede des proprietes importantes. High Quality Content by WIKIPEDIA articles! Par exemple, toute representation irreductible est isomorphe a une sous-representation de la representation reguliere.
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Similarly, an affine representation of a Lie algebra g on A is a Lie algebra homomorphism from g to the Lie algebra aff(A) of the affine group of A. An example is the action of the Euclidean group E(n) upon the Euclidean space En. Since the affine group in dimension n is a matrix group in dimension n + 1, an affine representation may be thought of as a particular kind of linear representation.
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