. "\u041F\u0440\u0438\u0454\u0434\u043D\u0430\u043D\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F \u0433\u0440\u0443\u043F\u0438 \u041B\u0456"@uk . . "In matematica, la rappresentazione aggiunta (o azione aggiunta) di un gruppo di Lie \u00E8 un modo di rappresentare gli elementi del gruppo come trasformazioni lineari dell'algebra di Lie del gruppo, considerata come uno spazio vettoriale. Ad esempio, dato il gruppo , il gruppo di Lie di matrici invertibili reali n per n, allora la rappresentazione aggiunta \u00E8 l'omomorfismo di gruppo che manda una matrice n-per-n invertibile a un endomorfismo dello spazio vettoriale di tutte le trasformazioni lineari di definito da ."@it . "In der Mathematik spielen die adjungierten Darstellungen von Lie-Gruppen und Lie-Algebren eine wichtige Rolle in Differentialgeometrie, Darstellungstheorie und Mathematischer Physik."@de . . "\u5728\u6578\u5B78\u4E2D\uFF0C\u4E00\u500B\u674E\u7FA4 G \u7684\u4F34\u96A8\u8868\u793A\uFF08adjoint representation\uFF09\u6216\u4F34\u96A8\u4F5C\u7528\uFF08adjoint action\uFF09\u662F G \u5728\u5B83\u81EA\u8EAB\u7684\u674E\u4EE3\u6578\u4E0A\u7684\u81EA\u7136\u8868\u793A\u3002\u9019\u500B\u8868\u793A\u662F\u7FA4 G \u5728\u81EA\u8EAB\u4E0A\u7684\u5171\u8EDB\u4F5C\u7528\u7684\u7DDA\u6027\u5316\u5F62\u5F0F\u3002"@zh . . . "Em matem\u00E1tica, a representa\u00E7\u00E3o adjunta (ou a\u00E7\u00E3o adjunta) de um grupo de Lie G \u00E9 uma forma de representar os elementos do grupo como transforma\u00E7\u00F5es lineares do grupo de \u00E1lgebra de Lie, considerado como um espa\u00E7o vetorial. Por exemplo, no caso em que G \u00E9 o grupo de Lie de matrizes invers\u00EDveis de tamanho n, GL(n), a \u00E1lgebra de Lie \u00E9 o espa\u00E7o vetorial de todas (n\u00E3o necessariamente invers\u00EDvel) matrizes n-por-n. Portanto, neste caso, a representa\u00E7\u00E3o adjunta \u00E9 o espa\u00E7o vetorial de matrizes n-por-n, e qualquer elemento g em GL(n) que atua como uma transforma\u00E7\u00E3o linear deste espa\u00E7o vetorial dada pela conjuga\u00E7\u00E3o: ."@pt . . . . . . "Repr\u00E9sentation adjointe"@fr . . "Adjungierte Darstellung"@de . . . "\uB9AC \uAD70\uB860\uC5D0\uC11C \uB538\uB9BC\uD45C\uD604(-\u8868\u73FE, \uC601\uC5B4: adjoint representation)\uC740 \uC5B4\uB5A4 \uB9AC \uAD70\uC774 \uC2A4\uC2A4\uB85C\uC758 \uB9AC \uB300\uC218 \uC704\uC5D0 \uAC00\uC9C0\uB294 \uD45C\uC900\uC801\uC778 \uD45C\uD604\uC774\uB2E4."@ko . . . . . . . . . "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: ."@en . . . . . . . "Rappresentazione aggiunta"@it . "\uB9AC \uAD70\uB860\uC5D0\uC11C \uB538\uB9BC\uD45C\uD604(-\u8868\u73FE, \uC601\uC5B4: adjoint representation)\uC740 \uC5B4\uB5A4 \uB9AC \uAD70\uC774 \uC2A4\uC2A4\uB85C\uC758 \uB9AC \uB300\uC218 \uC704\uC5D0 \uAC00\uC9C0\uB294 \uD45C\uC900\uC801\uC778 \uD45C\uD604\uC774\uB2E4."@ko . . . . . . "\u0423 \u0442\u0435\u043E\u0440\u0456\u0457 \u0433\u0440\u0443\u043F \u041B\u0456 \u043F\u0440\u0438\u0454\u0434\u043D\u0430\u043D\u0438\u043C \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F\u043C \u0433\u0440\u0443\u043F\u0438 \u041B\u0456 G \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u0433\u0440\u0443\u043F\u0438, \u044F\u043A \u043B\u0456\u043D\u0456\u0439\u043D\u0438\u0445 \u0432\u0456\u0434\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u044C \u043D\u0430 \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u043D\u0456\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0456 \u041B\u0456. \u0414\u0430\u043D\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F \u0454 \u0433\u043E\u043C\u043E\u043C\u043E\u0440\u0444\u0456\u0437\u043C\u043E\u043C \u0433\u0440\u0443\u043F \u041B\u0456. \u0419\u043E\u0433\u043E \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B \u0454 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F\u043C \u0430\u043B\u0433\u0435\u0431\u0440\u0438 \u041B\u0456, \u0449\u043E \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043F\u0440\u0438\u0454\u0434\u043D\u0430\u043D\u0438\u043C \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F\u043C \u0430\u043B\u0433\u0435\u0431\u0440\u0438 \u041B\u0456."@uk . . . . . . . . . . . . . . "En math\u00E9matiques, il existe deux notions de repr\u00E9sentations adjointes : \n* la repr\u00E9sentation adjointe d'un groupe de Lie sur son alg\u00E8bre de Lie, \n* la repr\u00E9sentation adjointe d'une alg\u00E8bre de Lie sur elle-m\u00EAme. Alors que la premi\u00E8re est une repr\u00E9sentation de groupe, la seconde est une repr\u00E9sentation d'alg\u00E8bre."@fr . . "In matematica, la rappresentazione aggiunta (o azione aggiunta) di un gruppo di Lie \u00E8 un modo di rappresentare gli elementi del gruppo come trasformazioni lineari dell'algebra di Lie del gruppo, considerata come uno spazio vettoriale. Ad esempio, dato il gruppo , il gruppo di Lie di matrici invertibili reali n per n, allora la rappresentazione aggiunta \u00E8 l'omomorfismo di gruppo che manda una matrice n-per-n invertibile a un endomorfismo dello spazio vettoriale di tutte le trasformazioni lineari di definito da . Per ogni gruppo di Lie, questa rappresentazione naturale si ottiene linearizzando (cio\u00E8 prendendo il differenziale) l'azione del gruppo su se stesso per coniugazione. La rappresentazione aggiunta pu\u00F2 essere definita per gruppi algebrici lineari su campi arbitrari."@it . . . . . . "En math\u00E9matiques, il existe deux notions de repr\u00E9sentations adjointes : \n* la repr\u00E9sentation adjointe d'un groupe de Lie sur son alg\u00E8bre de Lie, \n* la repr\u00E9sentation adjointe d'une alg\u00E8bre de Lie sur elle-m\u00EAme. Alors que la premi\u00E8re est une repr\u00E9sentation de groupe, la seconde est une repr\u00E9sentation d'alg\u00E8bre."@fr . . . . "\u041F\u0440\u0438\u0441\u043E\u0435\u0434\u0438\u043D\u0451\u043D\u043D\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u041B\u0438 \u2014 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u041B\u0438 \u043D\u0430 \u0441\u0432\u043E\u0435\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0435 \u041B\u0438.\u041E\u0431\u044B\u0447\u043D\u043E \u043E\u0431\u043E\u0437\u043D\u0430\u0447\u0430\u0435\u0442\u0441\u044F ."@ru . . . . "\u041F\u0440\u0438\u0441\u043E\u0435\u0434\u0438\u043D\u0451\u043D\u043D\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u041B\u0438"@ru . "\u4F34\u968F\u8868\u793A"@zh . . . "\u30EA\u30FC\u7FA4\u306E\u30EA\u30FC\u74B0\u4E0A\u3078\u306E\u968F\u4F34\u8868\u73FE\uFF08\u305A\u3044\u306F\u3093\u3072\u3087\u3046\u3052\u3093\u3001\u82F1: adjoint representation\uFF09\u3068\u306F\u3001\u30EA\u30FC\u7FA4\u306E\u5143\u3092\u30EA\u30FC\u74B0\u306E\u3042\u308B\u7A2E\u306E\u7DDA\u578B\u5909\u63DB\u3068\u3057\u3066\u8868\u3057\u305F\u3082\u306E\u3092\u3044\u3046\u3002"@ja . "\u041F\u0440\u0438\u0441\u043E\u0435\u0434\u0438\u043D\u0451\u043D\u043D\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u041B\u0438 \u2014 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u0433\u0440\u0443\u043F\u043F\u044B \u041B\u0438 \u043D\u0430 \u0441\u0432\u043E\u0435\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0435 \u041B\u0438.\u041E\u0431\u044B\u0447\u043D\u043E \u043E\u0431\u043E\u0437\u043D\u0430\u0447\u0430\u0435\u0442\u0441\u044F ."@ru . . . . "\u968F\u4F34\u8868\u73FE"@ja . . . . . "\u30EA\u30FC\u7FA4\u306E\u30EA\u30FC\u74B0\u4E0A\u3078\u306E\u968F\u4F34\u8868\u73FE\uFF08\u305A\u3044\u306F\u3093\u3072\u3087\u3046\u3052\u3093\u3001\u82F1: adjoint representation\uFF09\u3068\u306F\u3001\u30EA\u30FC\u7FA4\u306E\u5143\u3092\u30EA\u30FC\u74B0\u306E\u3042\u308B\u7A2E\u306E\u7DDA\u578B\u5909\u63DB\u3068\u3057\u3066\u8868\u3057\u305F\u3082\u306E\u3092\u3044\u3046\u3002"@ja . "20832"^^ . . . . "302188"^^ . "1101102744"^^ . . . . . "Representa\u00E7\u00E3o adjunta (grupo de Lie)"@pt . . . . . . "\u5728\u6578\u5B78\u4E2D\uFF0C\u4E00\u500B\u674E\u7FA4 G \u7684\u4F34\u96A8\u8868\u793A\uFF08adjoint representation\uFF09\u6216\u4F34\u96A8\u4F5C\u7528\uFF08adjoint action\uFF09\u662F G \u5728\u5B83\u81EA\u8EAB\u7684\u674E\u4EE3\u6578\u4E0A\u7684\u81EA\u7136\u8868\u793A\u3002\u9019\u500B\u8868\u793A\u662F\u7FA4 G \u5728\u81EA\u8EAB\u4E0A\u7684\u5171\u8EDB\u4F5C\u7528\u7684\u7DDA\u6027\u5316\u5F62\u5F0F\u3002"@zh . "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: . For any Lie group, this natural representation is obtained by linearizing (i.e. taking the differential of) the action of G on itself by conjugation. The adjoint representation can be defined for linear algebraic groups over arbitrary fields."@en . . . "Em matem\u00E1tica, a representa\u00E7\u00E3o adjunta (ou a\u00E7\u00E3o adjunta) de um grupo de Lie G \u00E9 uma forma de representar os elementos do grupo como transforma\u00E7\u00F5es lineares do grupo de \u00E1lgebra de Lie, considerado como um espa\u00E7o vetorial. Por exemplo, no caso em que G \u00E9 o grupo de Lie de matrizes invers\u00EDveis de tamanho n, GL(n), a \u00E1lgebra de Lie \u00E9 o espa\u00E7o vetorial de todas (n\u00E3o necessariamente invers\u00EDvel) matrizes n-por-n. Portanto, neste caso, a representa\u00E7\u00E3o adjunta \u00E9 o espa\u00E7o vetorial de matrizes n-por-n, e qualquer elemento g em GL(n) que atua como uma transforma\u00E7\u00E3o linear deste espa\u00E7o vetorial dada pela conjuga\u00E7\u00E3o: ."@pt . . . . . "Adjoint representation"@en . "\u0423 \u0442\u0435\u043E\u0440\u0456\u0457 \u0433\u0440\u0443\u043F \u041B\u0456 \u043F\u0440\u0438\u0454\u0434\u043D\u0430\u043D\u0438\u043C \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F\u043C \u0433\u0440\u0443\u043F\u0438 \u041B\u0456 G \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F \u0435\u043B\u0435\u043C\u0435\u043D\u0442\u0456\u0432 \u0433\u0440\u0443\u043F\u0438, \u044F\u043A \u043B\u0456\u043D\u0456\u0439\u043D\u0438\u0445 \u0432\u0456\u0434\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u044C \u043D\u0430 \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u043D\u0456\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0456 \u041B\u0456. \u0414\u0430\u043D\u0435 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F \u0454 \u0433\u043E\u043C\u043E\u043C\u043E\u0440\u0444\u0456\u0437\u043C\u043E\u043C \u0433\u0440\u0443\u043F \u041B\u0456. \u0419\u043E\u0433\u043E \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B \u0454 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F\u043C \u0430\u043B\u0433\u0435\u0431\u0440\u0438 \u041B\u0456, \u0449\u043E \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043F\u0440\u0438\u0454\u0434\u043D\u0430\u043D\u0438\u043C \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u043D\u044F\u043C \u0430\u043B\u0433\u0435\u0431\u0440\u0438 \u041B\u0456."@uk . . . . . . . . "\uB538\uB9BC\uD45C\uD604"@ko . . . . . . "In der Mathematik spielen die adjungierten Darstellungen von Lie-Gruppen und Lie-Algebren eine wichtige Rolle in Differentialgeometrie, Darstellungstheorie und Mathematischer Physik."@de . . . .