. . . . . "\u0422\u043E\u0442\u043E\u0436\u043D\u0456\u0441\u0442\u044C \u042F\u043A\u043E\u0431\u0456"@uk . "Em matem\u00E1tica, a identidade de Jacobi \u00E9 a propriedade que uma opera\u00E7\u00E3o bin\u00E1ria pode satisfazer em termos com a ordem de avalia\u00E7\u00E3o para a opera\u00E7\u00E3o dada. A diferen\u00E7a das opera\u00E7\u00F5es associativas, o comportamento na ordem de avalia\u00E7\u00E3o \u00E9 importante para as opera\u00E7\u00F5es que satisfazem a identidade de Jacobi. A identidade foi denominada em honra ao matem\u00E1tico alem\u00E3o Carl Gustav Jakob Jacobi (1804-1851)."@pt . "Dalam matematika, identitas Jacobi adalah sifat dari operasi biner yang menjelaskan bagaimana urutan evaluasi, penempatan tanda kurung dalam beberapa produk, mempengaruhi hasil operasi. Sebaliknya, untuk operasi dengan sifat asosiatif, urutan evaluasi memberikan hasil yang sama (tidak menggunakan tanda kurung dalam beberapa produk). Identitas ini dinamai matentikawan asal Jerman . dan operasi braket Lie keduanya memenuhi identitas Jacobi. Dalam , identitas Jacobi menggunakan . Dalam mekanika kuantum, digunakan oleh operasi komutator dengan ruang Hilbert dan ekuivalen dalam mekanika kuantum oleh Moyal."@in . . . . "Jacobi-Identit\u00E4t"@de . . . . "1120384091"^^ . "Relation de Jacobi"@fr . . "Identitat de Jacobi"@ca . "\u0411\u0456\u043B\u0456\u043D\u0456\u0439\u043D\u0430 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u044F \u043D\u0430 \u043B\u0456\u043D\u0456\u0439\u043D\u043E\u043C\u0443 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456 V \u0437\u0430\u0434\u043E\u0432\u043E\u043B\u044C\u043D\u044F\u0454 \u0442\u043E\u0442\u043E\u0436\u043D\u0456\u0441\u0442\u044C \u042F\u043A\u043E\u0431\u0456, \u044F\u043A\u0449\u043E: \u041D\u0430\u0437\u0432\u0430\u043D\u043E \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u041A\u0430\u0440\u043B\u0430 \u0413\u0443\u0441\u0442\u0430\u0432\u0430 \u042F\u043A\u043E\u0431\u0456.\u041F\u043E\u043D\u044F\u0442\u0442\u044F \u0442\u043E\u0442\u043E\u0436\u043D\u043E\u0441\u0442\u0456 \u042F\u043A\u043E\u0431\u0456 \u0437\u0430\u0437\u0432\u0438\u0447\u0430\u0439 \u043F\u043E\u0432'\u044F\u0437\u0430\u043D\u0435 \u0437 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u043C\u0438 \u041B\u0456."@uk . . . . . "In der Mathematik erf\u00FCllt eine bilineare Abbildung auf dem Vektorraum die Jacobi-Identit\u00E4t (nach Carl Jacobi), falls gilt: f\u00FCr alle . Ist die bilineare Abbildung zus\u00E4tzlich antisymmetrisch, so handelt es sich um eine Lie-Klammer. Wichtige Beispiele sind der Kommutator linearer Abbildungen, das Vektorprodukt und die Poisson-Klammer."@de . "Dalam matematika, identitas Jacobi adalah sifat dari operasi biner yang menjelaskan bagaimana urutan evaluasi, penempatan tanda kurung dalam beberapa produk, mempengaruhi hasil operasi. Sebaliknya, untuk operasi dengan sifat asosiatif, urutan evaluasi memberikan hasil yang sama (tidak menggunakan tanda kurung dalam beberapa produk). Identitas ini dinamai matentikawan asal Jerman ."@in . . . "\u0422\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u043E \u042F\u043A\u043E\u0431\u0438 \u2014 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u043E \u043D\u0430 \u0431\u0438\u043B\u0438\u043D\u0435\u0439\u043D\u0443\u044E \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044E \u043D\u0430 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u043C \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0435 . \u0418\u043C\u0435\u0435\u0442 \u0441\u043B\u0435\u0434\u0443\u044E\u0449\u0438\u0439 \u0432\u0438\u0434: \u041D\u0430\u0437\u0432\u0430\u043D\u043E \u0432 \u0447\u0435\u0441\u0442\u044C \u041A\u0430\u0440\u043B\u0430 \u0413\u0443\u0441\u0442\u0430\u0432\u0430 \u042F\u043A\u043E\u0431\u0438. \u041F\u043E\u043D\u044F\u0442\u0438\u0435 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u0430 \u042F\u043A\u043E\u0431\u0438 \u043E\u0431\u044B\u0447\u043D\u043E \u0441\u0432\u044F\u0437\u0430\u043D\u043E \u0441 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u043C\u0438 \u041B\u0438."@ru . . "La relation de Jacobi (ou identit\u00E9 de Jacobi), due \u00E0 Charles Gustave Jacob Jacobi, est la condition n\u00E9cessaire impos\u00E9e sur un espace vectoriel muni d'une application bilin\u00E9aire altern\u00E9e pour en faire une alg\u00E8bre de Lie ; on dit alors que l'application est un crochet de Lie. La relation de Jacobi s'\u00E9crit de la fa\u00E7on suivante :"@fr . "\u0422\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u043E \u042F\u043A\u043E\u0431\u0438"@ru . . . . . "294370"^^ . "In de wiskunde is de Jacobi-identiteit een eigenschap waar een binaire operatie aan kan voldoen en die bepaalt hoe de volgorde van evaluatie zich voor de gegeven operatie gedraagt. De volgorde van evaluatie is belangrijk voor operaties die aan de Jacobi-identiteit voldoen. Daarin verschillen deze operaties van associatieve operaties, waar de volgorde er niet toe doet. De identiteit is naar Carl Jacobi genoemd. Een binaire operatie op een verzameling , die een commutatieve binaire operatie bezit, voldoet aan de Jacobi-identiteit als De Jacobi-identiteit luidt in formule:"@nl . . . "\u0422\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u043E \u042F\u043A\u043E\u0431\u0438 \u2014 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u043E \u043D\u0430 \u0431\u0438\u043B\u0438\u043D\u0435\u0439\u043D\u0443\u044E \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u044E \u043D\u0430 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u043C \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0435 . \u0418\u043C\u0435\u0435\u0442 \u0441\u043B\u0435\u0434\u0443\u044E\u0449\u0438\u0439 \u0432\u0438\u0434: \u041D\u0430\u0437\u0432\u0430\u043D\u043E \u0432 \u0447\u0435\u0441\u0442\u044C \u041A\u0430\u0440\u043B\u0430 \u0413\u0443\u0441\u0442\u0430\u0432\u0430 \u042F\u043A\u043E\u0431\u0438. \u041F\u043E\u043D\u044F\u0442\u0438\u0435 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u0430 \u042F\u043A\u043E\u0431\u0438 \u043E\u0431\u044B\u0447\u043D\u043E \u0441\u0432\u044F\u0437\u0430\u043D\u043E \u0441 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u043C\u0438 \u041B\u0438."@ru . "Identidad de Jacobi"@es . . "\u30E4\u30B3\u30D3\u6052\u7B49\u5F0F"@ja . . . . . . . . . "In mathematics, the Jacobi identity is a property of a binary operation that describes how the order of evaluation, the placement of parentheses in a multiple product, affects the result of the operation. By contrast, for operations with the associative property, any order of evaluation gives the same result (parentheses in a multiple product are not needed). The identity is named after the German mathematician Carl Gustav Jakob Jacobi. The cross product and the Lie bracket operation both satisfy the Jacobi identity. In analytical mechanics, the Jacobi identity is satisfied by the Poisson brackets. In quantum mechanics, it is satisfied by operator commutators on a Hilbert space and equivalently in the phase space formulation of quantum mechanics by the Moyal bracket."@en . . "\u96C5\u53EF\u6BD4\u6052\u7B49\u5F0F"@zh . . "\u6570\u5B66\u306B\u304A\u3051\u308B\u30E4\u30B3\u30D3\u6052\u7B49\u5F0F\uFF08\u30E4\u30B3\u30D3\u3053\u3046\u3068\u3046\u3057\u304D\u3001\u82F1\u8A9E: Jacobi identity\uFF09\u3068\u306F\u3001\u4E8C\u9805\u6F14\u7B97\u306B\u5BFE\u3057\u3066\u8003\u3048\u3089\u308C\u308B\u6027\u8CEA\u306E\u4E00\u3064\u3002\u540D\u524D\u306F\u30C9\u30A4\u30C4\u306E\u6570\u5B66\u8005\u30AB\u30FC\u30EB\u30FB\u30B0\u30B9\u30BF\u30D5\u30FB\u30E4\u30B3\u30D6\u30FB\u30E4\u30B3\u30D3\u306B\u7531\u6765\u3059\u308B\u3002"@ja . "\uC57C\uCF54\uBE44 \uD56D\uB4F1\uC2DD"@ko . . . . . . . . . . . . "\uC57C\uCF54\uBE44 \uD56D\uB4F1\uC2DD( - \u6052\u7B49\u5F0F, \uB3C5\uC77C\uC5B4: Jacobi-Identit\u00E4t, \uC601\uC5B4: Jacobi identity)\uC740 \uC774\uD56D \uC5F0\uC0B0\uC790\uAC00 \uC5F0\uC0B0 \uC21C\uC11C\uC5D0 \uB300\uD574 \uAC00\uC9C0\uACE0 \uC788\uB294 \uD2B9\uC815\uD55C \uC131\uC9C8\uC744 \uAC00\uB9AC\uD0A8\uB2E4. \uAD50\uD658\uBC95\uCE59\uC774 \uC131\uB9BD\uD558\uB294 \uC774\uD56D \uC5F0\uC0B0\uC790 \uAC00 \uC8FC\uC5B4\uC838 \uC788\uC744 \uB54C, \uC774\uD56D \uC5F0\uC0B0\uC790 \uAC00 \uD56D\uC0C1 \uB2E4\uC74C \uC2DD\uC744 \uB9CC\uC871\uD560 \uACBD\uC6B0 \uC57C\uCF54\uBE44 \uD56D\uB4F1\uC2DD\uC744 \uB9CC\uC871\uD55C\uB2E4\uACE0 \uC815\uC758\uD55C\uB2E4."@ko . . "En matem\u00E1ticas, la identidad de Jacobi es la propiedad que una operaci\u00F3n binaria puede satisfacer en t\u00E9rminos con el orden de evaluaci\u00F3n para la operaci\u00F3n dada. A diferencia de las operaciones asociativas, el comportamiento en el orden de evaluaci\u00F3n es importante para las operaciones que satisfacen la identidad de Jacobi. La identidad fue llamada en honor al matem\u00E1tico alem\u00E1n Carl Gustav Jakob Jacobi (1804-1851)."@es . "Jacobi-identiteit"@nl . . . . . . . . "In matematica e in fisica, l'identit\u00E0 di Jacobi, il cui nome si deve a Carl Gustav Jakob Jacobi, \u00E8 una propriet\u00E0 di bilinearit\u00E0 la quale dipende dall'ordine di valutazione dell'operazione data. Diversamente dalle operazioni associative, \u00E8 importante l'ordine di valutazione delle quantit\u00E0 che devono soddisfare all'identit\u00E0 di Jacobi."@it . . "Jacobi-identiteten, eller Jacobis identitet, inneb\u00E4r inom matematiken att en bilinj\u00E4r avbildning p\u00E5 vektorrummet uppfyller: . \u00C4r den bilinj\u00E4ra avbildningen dessutom antisymmetrisk r\u00F6r det sig om en lieparentes. Viktiga exempel \u00E4r: \n* Kommutatorer f\u00F6r linj\u00E4ra avbildningar: \n* Vektorprodukt: \n* : Jacobi-identiteten \u00E4r uppkallad efter den tyske matematikern Carl Jacobi."@sv . . . . "Jacobi identity"@en . . "Jacobi-identiteten, eller Jacobis identitet, inneb\u00E4r inom matematiken att en bilinj\u00E4r avbildning p\u00E5 vektorrummet uppfyller: . \u00C4r den bilinj\u00E4ra avbildningen dessutom antisymmetrisk r\u00F6r det sig om en lieparentes. Viktiga exempel \u00E4r: \n* Kommutatorer f\u00F6r linj\u00E4ra avbildningar: \n* Vektorprodukt: \n* : Jacobi-identiteten \u00E4r uppkallad efter den tyske matematikern Carl Jacobi."@sv . . . "Identidade de Jacobi"@pt . . "Identit\u00E0 di Jacobi"@it . . . . "Identitas Jacobi"@in . . "\u0411\u0456\u043B\u0456\u043D\u0456\u0439\u043D\u0430 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u044F \u043D\u0430 \u043B\u0456\u043D\u0456\u0439\u043D\u043E\u043C\u0443 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456 V \u0437\u0430\u0434\u043E\u0432\u043E\u043B\u044C\u043D\u044F\u0454 \u0442\u043E\u0442\u043E\u0436\u043D\u0456\u0441\u0442\u044C \u042F\u043A\u043E\u0431\u0456, \u044F\u043A\u0449\u043E: \u041D\u0430\u0437\u0432\u0430\u043D\u043E \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u041A\u0430\u0440\u043B\u0430 \u0413\u0443\u0441\u0442\u0430\u0432\u0430 \u042F\u043A\u043E\u0431\u0456.\u041F\u043E\u043D\u044F\u0442\u0442\u044F \u0442\u043E\u0442\u043E\u0436\u043D\u043E\u0441\u0442\u0456 \u042F\u043A\u043E\u0431\u0456 \u0437\u0430\u0437\u0432\u0438\u0447\u0430\u0439 \u043F\u043E\u0432'\u044F\u0437\u0430\u043D\u0435 \u0437 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u043C\u0438 \u041B\u0456."@uk . . . "\u96C5\u53EF\u6BD4\u6052\u7B49\u5F0F\u5C31\u662F\u4E0B\u5217\u7B49\u5F0F\uFF1A"@zh . "En matem\u00E1ticas, la identidad de Jacobi es la propiedad que una operaci\u00F3n binaria puede satisfacer en t\u00E9rminos con el orden de evaluaci\u00F3n para la operaci\u00F3n dada. A diferencia de las operaciones asociativas, el comportamiento en el orden de evaluaci\u00F3n es importante para las operaciones que satisfacen la identidad de Jacobi. La identidad fue llamada en honor al matem\u00E1tico alem\u00E1n Carl Gustav Jakob Jacobi (1804-1851)."@es . . . . "Em matem\u00E1tica, a identidade de Jacobi \u00E9 a propriedade que uma opera\u00E7\u00E3o bin\u00E1ria pode satisfazer em termos com a ordem de avalia\u00E7\u00E3o para a opera\u00E7\u00E3o dada. A diferen\u00E7a das opera\u00E7\u00F5es associativas, o comportamento na ordem de avalia\u00E7\u00E3o \u00E9 importante para as opera\u00E7\u00F5es que satisfazem a identidade de Jacobi. A identidade foi denominada em honra ao matem\u00E1tico alem\u00E3o Carl Gustav Jakob Jacobi (1804-1851)."@pt . "6611"^^ . "Si es defineix el commutador de dos operadors A i B com La identitat de Jacobi \u00E9s el nom de l'equaci\u00F3 seg\u00FCent, anomenada aix\u00ED en honor de Carl Gustav Jacob Jacobi: Les \u00E0lgebres de Lie s\u00F3n l'exemple primari d'una \u00E0lgebra que satisf\u00E0 la identitat de Jacobi. Per\u00F2 observis que una \u00E0lgebra pot satisfer la identitat de Jacobi i no per aix\u00F2 ser anticommutativa."@ca . "La relation de Jacobi (ou identit\u00E9 de Jacobi), due \u00E0 Charles Gustave Jacob Jacobi, est la condition n\u00E9cessaire impos\u00E9e sur un espace vectoriel muni d'une application bilin\u00E9aire altern\u00E9e pour en faire une alg\u00E8bre de Lie ; on dit alors que l'application est un crochet de Lie. La relation de Jacobi s'\u00E9crit de la fa\u00E7on suivante :"@fr . . . . "In der Mathematik erf\u00FCllt eine bilineare Abbildung auf dem Vektorraum die Jacobi-Identit\u00E4t (nach Carl Jacobi), falls gilt: f\u00FCr alle . Ist die bilineare Abbildung zus\u00E4tzlich antisymmetrisch, so handelt es sich um eine Lie-Klammer. Wichtige Beispiele sind der Kommutator linearer Abbildungen, das Vektorprodukt und die Poisson-Klammer."@de . . "\u96C5\u53EF\u6BD4\u6052\u7B49\u5F0F\u5C31\u662F\u4E0B\u5217\u7B49\u5F0F\uFF1A"@zh . . "Jacobi-identiteten"@sv . . . . . . "\u6570\u5B66\u306B\u304A\u3051\u308B\u30E4\u30B3\u30D3\u6052\u7B49\u5F0F\uFF08\u30E4\u30B3\u30D3\u3053\u3046\u3068\u3046\u3057\u304D\u3001\u82F1\u8A9E: Jacobi identity\uFF09\u3068\u306F\u3001\u4E8C\u9805\u6F14\u7B97\u306B\u5BFE\u3057\u3066\u8003\u3048\u3089\u308C\u308B\u6027\u8CEA\u306E\u4E00\u3064\u3002\u540D\u524D\u306F\u30C9\u30A4\u30C4\u306E\u6570\u5B66\u8005\u30AB\u30FC\u30EB\u30FB\u30B0\u30B9\u30BF\u30D5\u30FB\u30E4\u30B3\u30D6\u30FB\u30E4\u30B3\u30D3\u306B\u7531\u6765\u3059\u308B\u3002"@ja . . "In mathematics, the Jacobi identity is a property of a binary operation that describes how the order of evaluation, the placement of parentheses in a multiple product, affects the result of the operation. By contrast, for operations with the associative property, any order of evaluation gives the same result (parentheses in a multiple product are not needed). The identity is named after the German mathematician Carl Gustav Jakob Jacobi."@en . "\uC57C\uCF54\uBE44 \uD56D\uB4F1\uC2DD( - \u6052\u7B49\u5F0F, \uB3C5\uC77C\uC5B4: Jacobi-Identit\u00E4t, \uC601\uC5B4: Jacobi identity)\uC740 \uC774\uD56D \uC5F0\uC0B0\uC790\uAC00 \uC5F0\uC0B0 \uC21C\uC11C\uC5D0 \uB300\uD574 \uAC00\uC9C0\uACE0 \uC788\uB294 \uD2B9\uC815\uD55C \uC131\uC9C8\uC744 \uAC00\uB9AC\uD0A8\uB2E4. \uAD50\uD658\uBC95\uCE59\uC774 \uC131\uB9BD\uD558\uB294 \uC774\uD56D \uC5F0\uC0B0\uC790 \uAC00 \uC8FC\uC5B4\uC838 \uC788\uC744 \uB54C, \uC774\uD56D \uC5F0\uC0B0\uC790 \uAC00 \uD56D\uC0C1 \uB2E4\uC74C \uC2DD\uC744 \uB9CC\uC871\uD560 \uACBD\uC6B0 \uC57C\uCF54\uBE44 \uD56D\uB4F1\uC2DD\uC744 \uB9CC\uC871\uD55C\uB2E4\uACE0 \uC815\uC758\uD55C\uB2E4."@ko . "In de wiskunde is de Jacobi-identiteit een eigenschap waar een binaire operatie aan kan voldoen en die bepaalt hoe de volgorde van evaluatie zich voor de gegeven operatie gedraagt. De volgorde van evaluatie is belangrijk voor operaties die aan de Jacobi-identiteit voldoen. Daarin verschillen deze operaties van associatieve operaties, waar de volgorde er niet toe doet. De identiteit is naar Carl Jacobi genoemd. Een binaire operatie op een verzameling , die een commutatieve binaire operatie bezit, voldoet aan de Jacobi-identiteit als In een lie-algebra zijn objecten die voldoen aan de Jacobi-identiteit infinitesimaal kleine bewegingen. Wanneer zij acteren op een operator met een infinitesimale beweging, is de verandering in de operator de commutator. De Jacobi-identiteit luidt in formule: Dat betekent dat 'de infinitesimale beweging van gevolgd door een infinitesimale beweging van , anders: , minus de infinitesimale beweging van gevolgd door de infinitesimale beweging van , of , is de infinitesimale beweging van , of , wanneer deze op een willekeurige infinitesimale beweging inwerkt. Zij zijn dus gelijk.'"@nl . . . "Si es defineix el commutador de dos operadors A i B com La identitat de Jacobi \u00E9s el nom de l'equaci\u00F3 seg\u00FCent, anomenada aix\u00ED en honor de Carl Gustav Jacob Jacobi: Les \u00E0lgebres de Lie s\u00F3n l'exemple primari d'una \u00E0lgebra que satisf\u00E0 la identitat de Jacobi. Per\u00F2 observis que una \u00E0lgebra pot satisfer la identitat de Jacobi i no per aix\u00F2 ser anticommutativa."@ca . . . . "In matematica e in fisica, l'identit\u00E0 di Jacobi, il cui nome si deve a Carl Gustav Jakob Jacobi, \u00E8 una propriet\u00E0 di bilinearit\u00E0 la quale dipende dall'ordine di valutazione dell'operazione data. Diversamente dalle operazioni associative, \u00E8 importante l'ordine di valutazione delle quantit\u00E0 che devono soddisfare all'identit\u00E0 di Jacobi."@it . .