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In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is , the Lie group of real n-by-n invertible matrices, then the adjoint representation is the group homomorphism that sends an invertible n-by-n matrix to an endomorphism of the vector space of all linear transformations of defined by: .

Attributes	Values
rdf:type	Thing
rdfs:label	Adjungierte Darstellung Adjoint representation Représentation adjointe 随伴表現 딸림표현 Representação adjunta (grupo de Lie) Присоединённое представление группы Ли Приєднане представлення групи Лі 伴随表示
rdfs:comment	In der Mathematik spielen die adjungierten Darstellungen von Lie-Gruppen und Lie-Algebren eine wichtige Rolle in Differentialgeometrie, Darstellungstheorie und Mathematischer Physik. En mathématiques, il existe deux notions de représentations adjointes : * la représentation adjointe d'un groupe de Lie sur son algèbre de Lie, * la représentation adjointe d'une algèbre de Lie sur elle-même. Alors que la première est une représentation de groupe, la seconde est une . リー群のリー環上への随伴表現（ずいはんひょうげん、英: adjoint representation）とは、リー群の元をリー環のある種の線型変換として表したものをいう。 리 군론에서, 딸림표현(-表現, 영어: adjoint representation)은 어떤 리 군이 스스로의 리 대수 위에 가지는 표준적인 표현이다. Em matemática, a representação adjunta (ou ação adjunta) de um grupo de Lie G é uma forma de representar os elementos do grupo como transformações lineares do grupo de álgebra de Lie, considerado como um espaço vetorial. Por exemplo, no caso em que G é o grupo de Lie de matrizes inversíveis de tamanho n, GL(n), a álgebra de Lie é o espaço vetorial de todas (não necessariamente inversível) matrizes n-por-n. Portanto, neste caso, a representação adjunta é o espaço vetorial de matrizes n-por-n, e qualquer elemento g em GL(n) que atua como uma transformação linear deste espaço vetorial dada pela conjugação: . Присоединённое представление группы Ли — линейное представление группы Ли на своей алгебре Ли.Обычно обозначается . 在數學中，一個李群 G 的伴隨表示（adjoint representation）或伴隨作用（adjoint action）是 G 在它自身的李代數上的自然表示。這個表示是群 G 在自身上的共軛作用的線性化形式。 У теорії груп Лі приєднаним представленням групи Лі G називається представлення елементів групи, як лінійних відображень на відповідній алгебрі Лі. Дане представлення є гомоморфізмом груп Лі. Його диференціал є представленням алгебри Лі, що називається приєднаним представленням алгебри Лі. In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is , the Lie group of real n-by-n invertible matrices, then the adjoint representation is the group homomorphism that sends an invertible n-by-n matrix to an endomorphism of the vector space of all linear transformations of defined by: .
rdfs:seeAlso	Representation theory
foaf:isPrimaryTopicOf	wikipedia-en:Adjoint_representation
dct:subject	Representation theory of Lie groups Lie groups
Wikipage page ID	302188(xsd:integer)
Wikipage revision ID	960435432(xsd:integer)
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sameAs	Adjoint representation Adjoint representation Adjoint representation Adjoint representation Adjoint representation Adjoint representation Adjoint representation Adjoint representation Adjoint representation Adjoint representation Adjoint representation Adjoint representation

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