. . . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570 (\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u3060\u3044\u3059\u3046\u3001\u82F1: Clifford algebra) \u306F\u7D50\u5408\u591A\u5143\u74B0\u306E\u4E00\u7A2E\u3067\u3042\u308B\u3002K-\u4EE3\u6570\u3068\u3057\u3066\u3001\u305D\u308C\u3089\u306F\u5B9F\u6570\u3001\u8907\u7D20\u6570\u3001\u56DB\u5143\u6570\u3001\u305D\u3057\u3066\u3044\u304F\u3064\u304B\u306E\u4ED6\u306E\u8D85\u8907\u7D20\u6570\u7CFB\u3092\u4E00\u822C\u5316\u3059\u308B\u3002\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570\u306E\u7406\u8AD6\u306F\u4E8C\u6B21\u5F62\u5F0F\u3068\u76F4\u4EA4\u5909\u63DB\u306E\u7406\u8AD6\u3068\u89AA\u5BC6\u306B\u95A2\u4FC2\u304C\u3042\u308B\u3002\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570\u306F\u5E7E\u4F55\u5B66\u3001\u7406\u8AD6\u7269\u7406\u5B66\u3001\u30C7\u30B8\u30BF\u30EB\u753B\u50CF\u51E6\u7406\u3092\u542B\u3080\u7A2E\u3005\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u91CD\u8981\u306A\u5FDC\u7528\u3092\u6301\u3064\u3002\u305D\u308C\u3089\u306F\u30A4\u30AE\u30EA\u30B9\u4EBA\u5E7E\u4F55\u5B66\u8005\u306B\u3061\u306A\u3093\u3067\u540D\u3065\u3051\u3089\u308C\u3066\u3044\u308B\u3002 \u6700\u3082\u3088\u304F\u77E5\u3089\u308C\u305F\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570\u3001\u3042\u308B\u3044\u306F\u76F4\u4EA4\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570 (\u3061\u3087\u3063\u3053\u3046\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u3060\u3044\u3059\u3046\u3001\u82F1: orthogonal Clifford algebra) \u306F\u3001\u30EA\u30FC\u30DE\u30F3\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570 (\u30EA\u30FC\u30DE\u30F3\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u3060\u3044\u3059\u3046\u3001\u82F1: Riemannian Clifford algebra) \u3068\u3082\u547C\u3070\u308C\u308B\u3002"@ja . . . . . . . . . . . . . . "\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570"@ja . . . . . . . . . . "In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing. They are named after the English mathematician William Kingdon Clifford. The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as (pseudo-)Riemannian Clifford algebras, as distinct from symplectic Clifford algebras."@en . . . . . . . . . . . . . . . . . . . . . "\u0410\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u043B\u0438\u0444\u0444\u043E\u0440\u0434\u0430 \u2014 \u0441\u043F\u0435\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0432\u0438\u0434\u0430 \u0430\u0441\u0441\u043E\u0446\u0438\u0430\u0442\u0438\u0432\u043D\u0430\u044F \u0430\u043B\u0433\u0435\u0431\u0440\u0430 \u0441 \u0435\u0434\u0438\u043D\u0438\u0446\u0435\u0439 \u043D\u0430\u0434 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u043C \u043A\u043E\u043C\u043C\u0443\u0442\u0430\u0442\u0438\u0432\u043D\u044B\u043C \u043A\u043E\u043B\u044C\u0446\u043E\u043C ( \u2014 \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E \u0438\u043B\u0438, \u0431\u043E\u043B\u0435\u0435 \u043E\u0431\u0449\u043E, \u0441\u0432\u043E\u0431\u043E\u0434\u043D\u044B\u0439 -\u043C\u043E\u0434\u0443\u043B\u044C) \u0441 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u043E\u043F\u0435\u0440\u0430\u0446\u0438\u0435\u0439 [\u00AB\u0443\u043C\u043D\u043E\u0436\u0435\u043D\u0438\u044F\u00BB], \u0441\u043E\u0432\u043F\u0430\u0434\u0430\u044E\u0449\u0435\u0439 \u0441 \u0437\u0430\u0434\u0430\u043D\u043D\u043E\u0439 \u043D\u0430 \u0431\u0438\u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0439 \u0444\u043E\u0440\u043C\u043E\u0439 ."@ru . "Cliffordalgebra \u00E4r en typ av vektoralgebra som kan betraktas som en generalisering av komplexa tal och kvaternioner. Algebran \u00E4r uppkallad efter William Kingdon Clifford. Geometrisk algebra, Cliffords ursprungliga algebra fr\u00E5n vilken begreppet Cliffordalgebra generaliserats, har en m\u00E4ngd till\u00E4mpningar inom datorgrafik och fysik."@sv . "\uD658\uB860\uC5D0\uC11C \uD074\uB9AC\uD37C\uB4DC \uB300\uC218(Clifford\u4EE3\u6578, \uC601\uC5B4: Clifford algebra)\uB294 \uC774\uCC28 \uD615\uC2DD\uC5D0 \uC758\uD558\uC5EC \uC815\uC758\uB418\uB294 \uACB0\uD569 \uB300\uC218\uC758 \uD55C \uC885\uB958\uC774\uB2E4. \uBCF5\uC18C\uC218\uCCB4\uC640 \uC0AC\uC6D0\uC218\uD658\uC758 \uC77C\uBC18\uD654\uC774\uBA70, \uC678\uB300\uC218\uC758 \uC591\uC790\uD654\uB85C \uC5EC\uAE38 \uC218 \uC788\uB2E4."@ko . . "p/c022460"@en . "1118571020"^^ . . . . . . . . . . "\u0410\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u043B\u0438\u0444\u0444\u043E\u0440\u0434\u0430"@ru . . . . . . . . . . . . . . . . . . "Je algebro, la al\u011Debro de Clifford estas asocieca al\u011Debro, generita de vektora spaco (a\u016D modulo), tia ke la kvadrato de \u0109iu unugrada elemento (t.e. elemento de la generinta vektora spaco) egalas la valoron de kvadrata formo."@eo . . . . . . . . . . . "1.5"^^ . . . "In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing. They are named after the English mathematician William Kingdon Clifford."@en . . "\u0410\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u043B\u0456\u0444\u043E\u0440\u0434\u0430 \u2014 \u0446\u0435 \u0443\u043D\u0456\u0442\u0430\u0440\u043D\u0430 \u0430\u0441\u043E\u0446\u0456\u0430\u0442\u0438\u0432\u043D\u0430 \u0430\u043B\u0433\u0435\u0431\u0440\u0430, \u0449\u043E \u043C\u0456\u0441\u0442\u0438\u0441\u044C \u0456 \u0443\u0442\u0432\u043E\u0440\u0435\u043D\u0430 \u0437\u0430 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0443 V \u0437 \u043A\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043D\u043E\u044E \u0444\u043E\u0440\u043C\u043E\u044E Q. \u0407\u0457 \u043C\u043E\u0436\u043D\u0430 \u0440\u043E\u0437\u0433\u043B\u044F\u0434\u0430\u0442\u0438 \u044F\u043A \u043E\u0434\u043D\u0435 \u0437 \u043C\u043E\u0436\u043B\u0438\u0432\u0438\u0445 \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0435\u043D\u044C \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u0442\u0430 \u043A\u0432\u0430\u0442\u0435\u0440\u043D\u0456\u043E\u043D\u0456\u0432. \u0422\u0435\u043E\u0440\u0456\u044F \u0430\u043B\u0433\u0435\u0431\u0440 \u041A\u043B\u0456\u0444\u043E\u0440\u0434\u0430 \u0442\u0456\u0441\u043D\u043E \u043F\u043E\u0432'\u044F\u0437\u0430\u043D\u0430 \u0437 \u0442\u0435\u043E\u0440\u0456\u0454\u044E \u043A\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043D\u0438\u0445 \u0444\u043E\u0440\u043C \u0456 . \u0410\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u043B\u0456\u0444\u0444\u043E\u0440\u0434\u0430 \u043C\u0430\u0454 \u0432\u0430\u0436\u043B\u0438\u0432\u0456 \u0434\u043E\u0434\u0430\u0442\u043A\u0438 \u0432 \u0440\u0456\u0437\u043D\u0438\u0445 \u043E\u0431\u043B\u0430\u0441\u0442\u044F\u0445, \u0432 \u0442\u043E\u043C\u0443 \u0447\u0438\u0441\u043B\u0456 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457 \u0442\u0430 \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u0447\u043D\u043E\u0457 \u0444\u0456\u0437\u0438\u043A\u0438. \u0412\u043E\u043D\u0430 \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0430\u043D\u0433\u043B\u0456\u0439\u0441\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0412\u0456\u043B\u044C\u044F\u043C\u0430 \u041A\u043B\u0456\u0444\u043E\u0440\u0434\u0430."@uk . . . . . "\uD658\uB860\uC5D0\uC11C \uD074\uB9AC\uD37C\uB4DC \uB300\uC218(Clifford\u4EE3\u6578, \uC601\uC5B4: Clifford algebra)\uB294 \uC774\uCC28 \uD615\uC2DD\uC5D0 \uC758\uD558\uC5EC \uC815\uC758\uB418\uB294 \uACB0\uD569 \uB300\uC218\uC758 \uD55C \uC885\uB958\uC774\uB2E4. \uBCF5\uC18C\uC218\uCCB4\uC640 \uC0AC\uC6D0\uC218\uD658\uC758 \uC77C\uBC18\uD654\uC774\uBA70, \uC678\uB300\uC218\uC758 \uC591\uC790\uD654\uB85C \uC5EC\uAE38 \uC218 \uC788\uB2E4."@ko . . "En math\u00E9matiques, l'alg\u00E8bre de Clifford est un objet d'alg\u00E8bre multilin\u00E9aire associ\u00E9 \u00E0 une forme quadratique. C'est une alg\u00E8bre associative sur un corps, permettant un type de calcul \u00E9tendu, englobant les vecteurs, les scalaires et des \u00AB multivecteurs \u00BB obtenus par produits de vecteurs, et avec une r\u00E8gle de calcul qui traduit la g\u00E9om\u00E9trie de la forme quadratique sous-jacente.Le nom de cette structure est un hommage au math\u00E9maticien anglais William Kingdon Clifford."@fr . . "\u00C1lgebra de Clifford"@es . "In de abstracte algebra is een clifford-algebra een unitaire (d.w.z. met eenheidselement) associatieve algebra die een uitbreiding vormt van de complexe getallen en de hypercomplexe getalsystemen. Clifford-algebra's zijn genoemd naar William Kingdon Clifford, die ze in 1878 ontdekte. De theorie van clifford-algebra's is nauw verbonden met de theorie van kwadratische vormen en orthogonale transformaties. Clifford-algebra's vinden brede toepassing in onder meer de meetkunde, de kwantumfysica, bij de definitie en voorstelling van spingroepen en spinoren, de bepaling van invarianten op varieteiten en de digitale beeldbewerking."@nl . . . . . "As \u00E1lgebras de Clifford s\u00E3o \u00E1lgebras associativas de import\u00E2ncia na matem\u00E1tica, em particular na teoria da forma quadr\u00E1tica e do grupo ortogonal e na f\u00EDsica. S\u00E3o nomeadas em homenagem a William Kingdon Clifford."@pt . "Cliffordalgebra \u00E4r en typ av vektoralgebra som kan betraktas som en generalisering av komplexa tal och kvaternioner. Algebran \u00E4r uppkallad efter William Kingdon Clifford. Geometrisk algebra, Cliffords ursprungliga algebra fr\u00E5n vilken begreppet Cliffordalgebra generaliserats, har en m\u00E4ngd till\u00E4mpningar inom datorgrafik och fysik."@sv . . "\u0410\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u043B\u0456\u0444\u043E\u0440\u0434\u0430"@uk . . . . . . "Clifford-algebra"@nl . . . . . . "In de abstracte algebra is een clifford-algebra een unitaire (d.w.z. met eenheidselement) associatieve algebra die een uitbreiding vormt van de complexe getallen en de hypercomplexe getalsystemen. Clifford-algebra's zijn genoemd naar William Kingdon Clifford, die ze in 1878 ontdekte."@nl . . . "En math\u00E9matiques, l'alg\u00E8bre de Clifford est un objet d'alg\u00E8bre multilin\u00E9aire associ\u00E9 \u00E0 une forme quadratique. C'est une alg\u00E8bre associative sur un corps, permettant un type de calcul \u00E9tendu, englobant les vecteurs, les scalaires et des \u00AB multivecteurs \u00BB obtenus par produits de vecteurs, et avec une r\u00E8gle de calcul qui traduit la g\u00E9om\u00E9trie de la forme quadratique sous-jacente.Le nom de cette structure est un hommage au math\u00E9maticien anglais William Kingdon Clifford. Les alg\u00E8bres de Clifford constituent l'une des g\u00E9n\u00E9ralisations possibles des nombres complexes et des quaternions. En math\u00E9matiques, elles offrent un cadre unificateur pour \u00E9tudier des probl\u00E8mes de g\u00E9om\u00E9trie tels que la th\u00E9orie des formes quadratiques, et les groupes orthogonaux et introduire les spineurs et la (en). Mais elles fournissent aussi un cadre de calcul pertinent \u00E0 de nombreux domaines physiques, des plus th\u00E9oriques (relativit\u00E9, m\u00E9canique quantique) aux plus appliqu\u00E9s (vision par ordinateur, robotique). Pour ces applications, une approche simplifi\u00E9e est parfois pratiqu\u00E9e, avec une introduction diff\u00E9rente, limit\u00E9e aux corps des r\u00E9els et complexes, ce qui conduit \u00E0 la structure tr\u00E8s proche d'alg\u00E8bre g\u00E9om\u00E9trique. Une certaine familiarit\u00E9 avec les bases de l'alg\u00E8bre multilin\u00E9aire sera tr\u00E8s utile \u00E0 la lecture de cet article.De nombreux r\u00E9sultats supposent que la caract\u00E9ristique du corps de base K n'est pas 2 (c'est-\u00E0-dire que la division par 2 est possible) ; on fait cette hypoth\u00E8se dans toute la suite, sauf dans une section d\u00E9di\u00E9e au cas particulier de la caract\u00E9ristique 2."@fr . . . "Clifford algebra"@en . . . . . . . . "\u6578\u5B78\u4E0A\uFF0C\u514B\u5229\u798F\u5FB7\u4EE3\u6570\uFF08Clifford algebra\uFF09\u662F\u7531\u5177\u6709\u4E8C\u6B21\u578B\u7684\u5411\u91CF\u7A7A\u9593\u751F\u6210\u7684\u55AE\u4F4D\u7D50\u5408\u4EE3\u6578\u3002\u4F5C\u70BA\u57DF\u4E0A\u7684\u4EE3\u6578\uFF0C\u5176\u63A8\u5EE3\u5BE6\u6578\u7CFB\u3001\u8907\u6578\u7CFB\u3001\u56DB\u5143\u6578\u7CFB\u7B49\u8D85\u8907\u6578\u7CFB\uFF0C\u4EE5\u53CA\u5916\u4EE3\u6570\u3002\u6B64\u4EE3\u6578\u7D50\u69CB\u5F97\u540D\u81EA\u82F1\u570B\u6578\u5B78\u5BB6\u5A01\u5EC9\u00B7\u91D1\u987F\u00B7\u514B\u5229\u798F\u5FB7\u3002 \u7814\u7A76\u514B\u91CC\u798F\u4EE3\u6570\u7684\u7406\u8AD6\u6709\u6642\u4E5F\u7A31\u70BA\u514B\u91CC\u798F\u4EE3\u6578\uFF0C\u5176\u8207\u4E8C\u6B21\u578B\u8AD6\u548C\u6B63\u4EA4\u7FA4\u7406\u8AD6\u7DCA\u5BC6\u806F\u7E6B\u3002\u5176\u5728\u51E0\u4F55\u3001\u7406\u8AD6\u7269\u7406\u3001\u4E2D\u6709\u5F88\u591A\u5E94\u7528\u3002\u5176\u4E3B\u8981\u8D21\u732E\u8005\u6709\uFF1A\u5A01\u5EC9\u00B7\u54C8\u5BC6\u987F\uFF08\u56DB\u5143\u6570\uFF09\uFF0C\u8D6B\u5C14\u66FC\u00B7\u683C\u62C9\u65AF\u66FC\uFF08\u5916\u4EE3\u6570\uFF09\uFF0C\u5A01\u5EC9\u00B7\u91D1\u987F\u00B7\u514B\u5229\u798F\u5FB7\uFF0C\u7B49\u3002 \u6700\u5E38\u898B\u7684\u514B\u91CC\u798F\u4EE3\u6578\u662F\u6B63\u4EA4\u514B\u91CC\u798F\u4EE3\u6578\uFF0C\u53C8\u7A31\uFF08\u507D\uFF09\u9ECE\u66FC\u514B\u91CC\u798F\u4EE3\u6578\u3002\u53E6\u4E00\u985E\u662F\u626D\u5C0D\u7A31\u514B\u91CC\u798F\u4EE3\u6578\u3002"@zh . . . . . . . . . "Las \u00E1lgebras de Clifford son \u00E1lgebras asociativas de importancia en matem\u00E1ticas, en particular en teor\u00EDa de la forma cuadr\u00E1tica y del grupo ortogonal y en la f\u00EDsica. Se nombran as\u00ED por William Kingdon Clifford."@es . . . . . . . "Cliffordalgebra"@sv . . . . . . . . . "Al\u011Debro de Clifford"@eo . . . . . . . "Die Clifford-Algebra ist ein nach William Kingdon Clifford benanntes mathematisches Objekt aus der Algebra, welches die komplexen und hyperkomplexen Zahlensysteme erweitert. Sie findet in der Differentialgeometrie sowie in der Quantenphysik Anwendung. Sie dient der Definition der Spin-Gruppe und ihrer Darstellungen, der Konstruktion von Spinorfeldern / -b\u00FCndeln, die wiederum zur Beschreibung von Elektronen und anderen Elementarteilchen wichtig sind, sowie zur Bestimmung von Invarianten auf Mannigfaltigkeiten."@de . . . . . . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570 (\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u3060\u3044\u3059\u3046\u3001\u82F1: Clifford algebra) \u306F\u7D50\u5408\u591A\u5143\u74B0\u306E\u4E00\u7A2E\u3067\u3042\u308B\u3002K-\u4EE3\u6570\u3068\u3057\u3066\u3001\u305D\u308C\u3089\u306F\u5B9F\u6570\u3001\u8907\u7D20\u6570\u3001\u56DB\u5143\u6570\u3001\u305D\u3057\u3066\u3044\u304F\u3064\u304B\u306E\u4ED6\u306E\u8D85\u8907\u7D20\u6570\u7CFB\u3092\u4E00\u822C\u5316\u3059\u308B\u3002\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570\u306E\u7406\u8AD6\u306F\u4E8C\u6B21\u5F62\u5F0F\u3068\u76F4\u4EA4\u5909\u63DB\u306E\u7406\u8AD6\u3068\u89AA\u5BC6\u306B\u95A2\u4FC2\u304C\u3042\u308B\u3002\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570\u306F\u5E7E\u4F55\u5B66\u3001\u7406\u8AD6\u7269\u7406\u5B66\u3001\u30C7\u30B8\u30BF\u30EB\u753B\u50CF\u51E6\u7406\u3092\u542B\u3080\u7A2E\u3005\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u91CD\u8981\u306A\u5FDC\u7528\u3092\u6301\u3064\u3002\u305D\u308C\u3089\u306F\u30A4\u30AE\u30EA\u30B9\u4EBA\u5E7E\u4F55\u5B66\u8005\u306B\u3061\u306A\u3093\u3067\u540D\u3065\u3051\u3089\u308C\u3066\u3044\u308B\u3002 \u6700\u3082\u3088\u304F\u77E5\u3089\u308C\u305F\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570\u3001\u3042\u308B\u3044\u306F\u76F4\u4EA4\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570 (\u3061\u3087\u3063\u3053\u3046\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u3060\u3044\u3059\u3046\u3001\u82F1: orthogonal Clifford algebra) \u306F\u3001\u30EA\u30FC\u30DE\u30F3\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u4EE3\u6570 (\u30EA\u30FC\u30DE\u30F3\u30AF\u30EA\u30D5\u30A9\u30FC\u30C9\u3060\u3044\u3059\u3046\u3001\u82F1: Riemannian Clifford algebra) \u3068\u3082\u547C\u3070\u308C\u308B\u3002"@ja . . . "Algebra di Clifford"@it . "\u514B\u5229\u798F\u5FB7\u4EE3\u6570"@zh . . . . . . . . . . . "Clifford-Algebra"@de . . . . . "63097"^^ . . . . . . . "\uD074\uB9AC\uD37C\uB4DC \uB300\uC218"@ko . "Las \u00E1lgebras de Clifford son \u00E1lgebras asociativas de importancia en matem\u00E1ticas, en particular en teor\u00EDa de la forma cuadr\u00E1tica y del grupo ortogonal y en la f\u00EDsica. Se nombran as\u00ED por William Kingdon Clifford."@es . . . "45305"^^ . . . . . "As \u00E1lgebras de Clifford s\u00E3o \u00E1lgebras associativas de import\u00E2ncia na matem\u00E1tica, em particular na teoria da forma quadr\u00E1tica e do grupo ortogonal e na f\u00EDsica. S\u00E3o nomeadas em homenagem a William Kingdon Clifford."@pt . . . . . . . "\u00C1lgebra de Clifford"@pt . . . . "Je algebro, la al\u011Debro de Clifford estas asocieca al\u011Debro, generita de vektora spaco (a\u016D modulo), tia ke la kvadrato de \u0109iu unugrada elemento (t.e. elemento de la generinta vektora spaco) egalas la valoron de kvadrata formo."@eo . . . . . . "In algebra lineare, un'algebra di Clifford \u00E8 una struttura algebrica che generalizza la nozione di numero complesso e di quaternione. Lo studio delle algebre di Clifford \u00E8 strettamente legato alla teoria delle forme quadratiche, e ha importanti applicazioni nella geometria e nella fisica teorica. Il loro nome deriva da quello del matematico William Kingdon Clifford che le introdusse nel 1878, partendo dallo studio di altri due oggetti algebrici analoghi, l'algebra dei quaternioni e le algebre di Grassmann."@it . . . . . . . . . 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"\u0410\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u043B\u0456\u0444\u043E\u0440\u0434\u0430 \u2014 \u0446\u0435 \u0443\u043D\u0456\u0442\u0430\u0440\u043D\u0430 \u0430\u0441\u043E\u0446\u0456\u0430\u0442\u0438\u0432\u043D\u0430 \u0430\u043B\u0433\u0435\u0431\u0440\u0430, \u0449\u043E \u043C\u0456\u0441\u0442\u0438\u0441\u044C \u0456 \u0443\u0442\u0432\u043E\u0440\u0435\u043D\u0430 \u0437\u0430 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0443 V \u0437 \u043A\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043D\u043E\u044E \u0444\u043E\u0440\u043C\u043E\u044E Q. \u0407\u0457 \u043C\u043E\u0436\u043D\u0430 \u0440\u043E\u0437\u0433\u043B\u044F\u0434\u0430\u0442\u0438 \u044F\u043A \u043E\u0434\u043D\u0435 \u0437 \u043C\u043E\u0436\u043B\u0438\u0432\u0438\u0445 \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0435\u043D\u044C \u043A\u043E\u043C\u043F\u043B\u0435\u043A\u0441\u043D\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u0442\u0430 \u043A\u0432\u0430\u0442\u0435\u0440\u043D\u0456\u043E\u043D\u0456\u0432. \u0422\u0435\u043E\u0440\u0456\u044F \u0430\u043B\u0433\u0435\u0431\u0440 \u041A\u043B\u0456\u0444\u043E\u0440\u0434\u0430 \u0442\u0456\u0441\u043D\u043E \u043F\u043E\u0432'\u044F\u0437\u0430\u043D\u0430 \u0437 \u0442\u0435\u043E\u0440\u0456\u0454\u044E \u043A\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043D\u0438\u0445 \u0444\u043E\u0440\u043C \u0456 . \u0410\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u043B\u0456\u0444\u0444\u043E\u0440\u0434\u0430 \u043C\u0430\u0454 \u0432\u0430\u0436\u043B\u0438\u0432\u0456 \u0434\u043E\u0434\u0430\u0442\u043A\u0438 \u0432 \u0440\u0456\u0437\u043D\u0438\u0445 \u043E\u0431\u043B\u0430\u0441\u0442\u044F\u0445, \u0432 \u0442\u043E\u043C\u0443 \u0447\u0438\u0441\u043B\u0456 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457 \u0442\u0430 \u0442\u0435\u043E\u0440\u0435\u0442\u0438\u0447\u043D\u043E\u0457 \u0444\u0456\u0437\u0438\u043A\u0438. \u0412\u043E\u043D\u0430 \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0430\u043D\u0433\u043B\u0456\u0439\u0441\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0412\u0456\u043B\u044C\u044F\u043C\u0430 \u041A\u043B\u0456\u0444\u043E\u0440\u0434\u0430."@uk . "Alg\u00E8bre de Clifford"@fr . . . . . . . "In algebra lineare, un'algebra di Clifford \u00E8 una struttura algebrica che generalizza la nozione di numero complesso e di quaternione. Lo studio delle algebre di Clifford \u00E8 strettamente legato alla teoria delle forme quadratiche, e ha importanti applicazioni nella geometria e nella fisica teorica. Il loro nome deriva da quello del matematico William Kingdon Clifford che le introdusse nel 1878, partendo dallo studio di altri due oggetti algebrici analoghi, l'algebra dei quaternioni e le algebre di Grassmann."@it . . . "Clifford algebra"@en . . . . . . . . . . . . . . . . . . . . . . . . . . "Die Clifford-Algebra ist ein nach William Kingdon Clifford benanntes mathematisches Objekt aus der Algebra, welches die komplexen und hyperkomplexen Zahlensysteme erweitert. Sie findet in der Differentialgeometrie sowie in der Quantenphysik Anwendung. Sie dient der Definition der Spin-Gruppe und ihrer Darstellungen, der Konstruktion von Spinorfeldern / -b\u00FCndeln, die wiederum zur Beschreibung von Elektronen und anderen Elementarteilchen wichtig sind, sowie zur Bestimmung von Invarianten auf Mannigfaltigkeiten."@de . . . 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