dbo:abstract |
In der Darstellungstheorie der Lie-Algebren, einem Teilgebiet der Mathematik, sind Gewichte gewisse lineare Abbildungen. Sie sind unter anderem deshalb von Bedeutung, weil Darstellungen von Lie-Gruppen und Lie-Algebren durch ihr höchstes Gewicht klassifiziert werden. (de) In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space. (en) 리 대수 이론에서, 무게(영어: weight)는 리 대수의 표현을 분류하는 일련의 수들이다. (ko) 表現論という数学の分野において,体 F 上の代数 A のウェイト(英: weight)とは,A から F へのである,あるいは同じことだが,A の F 上の1次元表現である.それは群のの代数の類似である.しかしながら,概念の重要性は,リー環の表現への,したがって代数群やリー群の表現への,その応用から生じる.この文脈では,表現のウェイトは固有値の概念の一般化であり,対応する固有空間はウェイト空間と呼ばれる. (ja) У теорії представлень вагою алгебри A над полем F називається гомоморфізм із A у поле F, або еквівалентно одновимірне представлення A над полем F. Воно є певною мірою аналогом мультиплікативного характеру групи. Подібне поняття також є для алгебр Лі, у цьому випадку вага представлення є узагальненням власного значення, і відповідний власний простір називається ваговим простором. (uk) |
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In der Darstellungstheorie der Lie-Algebren, einem Teilgebiet der Mathematik, sind Gewichte gewisse lineare Abbildungen. Sie sind unter anderem deshalb von Bedeutung, weil Darstellungen von Lie-Gruppen und Lie-Algebren durch ihr höchstes Gewicht klassifiziert werden. (de) In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space. (en) 리 대수 이론에서, 무게(영어: weight)는 리 대수의 표현을 분류하는 일련의 수들이다. (ko) 表現論という数学の分野において,体 F 上の代数 A のウェイト(英: weight)とは,A から F へのである,あるいは同じことだが,A の F 上の1次元表現である.それは群のの代数の類似である.しかしながら,概念の重要性は,リー環の表現への,したがって代数群やリー群の表現への,その応用から生じる.この文脈では,表現のウェイトは固有値の概念の一般化であり,対応する固有空間はウェイト空間と呼ばれる. (ja) У теорії представлень вагою алгебри A над полем F називається гомоморфізм із A у поле F, або еквівалентно одновимірне представлення A над полем F. Воно є певною мірою аналогом мультиплікативного характеру групи. Подібне поняття також є для алгебр Лі, у цьому випадку вага представлення є узагальненням власного значення, і відповідний власний простір називається ваговим простором. (uk) |
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Gewicht (Darstellung) (de) 무게 (표현론) (ko) ウェイト (表現論) (ja) Weight (representation theory) (en) Вага (теорія представлень) (uk) |
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