"In der Mathematik ist die Weyl-Gruppe ein wichtiges Hilfsmittel zur Untersuchung von Lie-Gruppen und Lie-Algebren und allgemeiner von Wurzelsystemen. Sie ist nach Hermann Weyl benannt, der 1925 ihre Bedeutung erkannte."@de . . "\uC218\uD559\uC5D0\uC11C \uBC14\uC77C \uAD70(\uC601\uC5B4: Weyl group)\uC740 \uADFC\uACC4\uC758 \uBC18\uC0AC \uC790\uAE30\uB3D9\uD615\uAD70\uC774\uB2E4. \uD5E4\uB974\uB9CC \uBC14\uC77C\uC758 \uC774\uB984\uC744 \uB544\uB2E4."@ko . . "In de groepentheorie, een deelgebied van de wiskunde, en met name in de theorie van de Lie-algebra's, is de weyl-groep van een wortelsysteem, , een deelgroep van de isometriegroep van dat wortelsysteem. De weyl-groep van een halfenkelvoudige lie-groep, een halfenkelvoudige lie-algebra, een halfenkelvoudige , enz. is de weyl-groep van het wortelstelsel van die groep of die algebra"@nl . . . . . . . . . . . . . . . . . "Weyl-groep"@nl . . . . . . . . . "Popov"@en . . . "21608"^^ . "A.S."@en . "\u30EF\u30A4\u30EB\u7FA4"@ja . . . . "En matem\u00E1ticas, en la teor\u00EDa de grupos y \u00E1lgebras de Lie, el grupo de Weyl de un es un subgrupo del grupo de isometr\u00EDas del sistema de ra\u00EDces. Concretamente, consiste en el grupo finito de reflexiones generado por las reflexiones con respecto a los hiperplanos ortogonales a las ra\u00EDces. Reciben este nombre en honor a Hermann Weyl."@es . . "En matem\u00E1ticas, en la teor\u00EDa de grupos y \u00E1lgebras de Lie, el grupo de Weyl de un es un subgrupo del grupo de isometr\u00EDas del sistema de ra\u00EDces. Concretamente, consiste en el grupo finito de reflexiones generado por las reflexiones con respecto a los hiperplanos ortogonales a las ra\u00EDces. Reciben este nombre en honor a Hermann Weyl."@es . . . . . "V.L."@en . "\u0413\u0440\u0443\u043F\u043F\u0430 \u0412\u0435\u0439\u043B\u044F"@ru . . "\u5916\u5C14\u7FA4"@zh . . "\u6570\u5B66\u3001\u7279\u306B\u30EA\u30FC\u74B0\u306E\u7406\u8AD6\u306B\u304A\u3044\u3066\u3001\u30EB\u30FC\u30C8\u7CFB \u03A6 \u306E\u30EF\u30A4\u30EB\u7FA4\uFF08\u82F1: Weyl group\uFF09\u306F\u3001\u30EB\u30FC\u30C8\u7CFB\u306E\u306E\u90E8\u5206\u7FA4\u3067\u3042\u308B\u3002\u5177\u4F53\u7684\u306B\u306F\u3001\u30EB\u30FC\u30C8\u306B\u76F4\u4EA4\u3059\u308B\u8D85\u5E73\u9762\u306B\u95A2\u3059\u308B\u93E1\u6620\u306B\u3088\u3063\u3066\u751F\u6210\u3055\u308C\u308B\u90E8\u5206\u7FA4\u306E\u3053\u3068\u3067\u3001\u305D\u306E\u3088\u3046\u306A\u3082\u306E\u3068\u3057\u3066\u3067\u3042\u308B\u3002\u62BD\u8C61\u7684\u306B\u306F\u3001\u30EF\u30A4\u30EB\u7FA4\u306F\u3067\u3042\u308A\u3001\u305D\u306E\u91CD\u8981\u306A\u4F8B\u3067\u3042\u308B\u3002 \u534A\u5358\u7D14\u30EA\u30FC\u7FA4\u3001\u534A\u5358\u7D14\u30EA\u30FC\u74B0\u3001\u7DDA\u578B\u4EE3\u6570\u7FA4\u3001\u306A\u3069\u306E\u30EF\u30A4\u30EB\u7FA4\u306F\u305D\u306E\u7FA4\u3042\u308B\u3044\u306F\u74B0\u306E\u30EB\u30FC\u30C8\u7CFB\u306E\u30EF\u30A4\u30EB\u7FA4\u3067\u3042\u308B\u3002 \u540D\u524D\u306F\u30D8\u30EB\u30DE\u30F3\u30FB\u30EF\u30A4\u30EB (Hermann Weyl) \u306B\u3061\u306A\u3080\u3002"@ja . . . . "In matematica, in particolare la teoria delle algebre di Lie, il gruppo di Weyl (dal nome di Hermann Weyl) di un sistema di radici \u00E8 un sottogruppo del gruppo di isometrie di quel sistema di radici. Nello specifico, \u00E8 il sottogruppo che si genera per riflessioni attraverso gli iperpiani ortogonali alle radici, e come tale \u00E8 un gruppo finito di riflessioni. Infatti risulta che la maggior parte dei gruppi di riflessione finiti sono gruppi di Weyl. [1] astratto, i gruppi di Weyl sono gruppi di Coxeter finiti e ne sono esempi importanti. Il gruppo di Weyl di un gruppo di Lie semisemplice, un'algebra di Lie semisemplice, un gruppo algebrico lineare semisemplice, ecc. \u00E8 il gruppo di Weyl del sistema di radici di quel gruppo o algebra ."@it . . "p/c026980"@en . . "Coxeter group"@en . . "Grupa Weyla"@pl . . . "In der Mathematik ist die Weyl-Gruppe ein wichtiges Hilfsmittel zur Untersuchung von Lie-Gruppen und Lie-Algebren und allgemeiner von Wurzelsystemen. Sie ist nach Hermann Weyl benannt, der 1925 ihre Bedeutung erkannte."@de . "\uC218\uD559\uC5D0\uC11C \uBC14\uC77C \uAD70(\uC601\uC5B4: Weyl group)\uC740 \uADFC\uACC4\uC758 \uBC18\uC0AC \uC790\uAE30\uB3D9\uD615\uAD70\uC774\uB2E4. \uD5E4\uB974\uB9CC \uBC14\uC77C\uC758 \uC774\uB984\uC744 \uB544\uB2E4."@ko . . . . . "En math\u00E9matiques, et en particulier dans la th\u00E9orie des alg\u00E8bres de Lie, le groupe de Weyl d'un syst\u00E8me de racines , nomm\u00E9 ainsi en hommage \u00E0 Hermann Weyl, est le sous-groupe du groupe d'isom\u00E9tries du syst\u00E8me de racines engendr\u00E9 par les r\u00E9flexions orthogonales par rapport aux hyperplans orthogonaux aux racines."@fr . . . "Weyl-Gruppe"@de . "In mathematics, in particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system \u03A6 is a subgroup of the isometry group of that root system. Specifically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to the roots, and as such is a finite reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these. The Weyl group of a semisimple Lie group, a semisimple Lie algebra, a semisimple linear algebraic group, etc. is the Weyl group of the root system of that group or algebra."@en . . . "CoxeterGroup"@en . . "Fedenko"@en . . . "In mathematics, in particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system \u03A6 is a subgroup of the isometry group of that root system. Specifically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to the roots, and as such is a finite reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these."@en . "\uBC14\uC77C \uAD70"@ko . . . . . . . . . . . . "2001"^^ . . . . . . "296332"^^ . . . . . . . . . "\u0413\u0440\u0443\u043F\u043F\u0430 \u0412\u0435\u0439\u043B\u044F \u2014 \u0433\u0440\u0443\u043F\u043F\u0430, \u043F\u043E\u0440\u043E\u0436\u0434\u0451\u043D\u043D\u0430\u044F \u043E\u0442\u0440\u0430\u0436\u0435\u043D\u0438\u044F\u043C\u0438 \u0432 \u0433\u0438\u043F\u0435\u0440\u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u044F\u0445, \u043E\u0440\u0442\u043E\u0433\u043E\u043D\u0430\u043B\u044C\u043D\u044B\u0445 \u043A \u043A\u043E\u0440\u043D\u044F\u043C \u043A\u043E\u0440\u043D\u0435\u0432\u043E\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u044B \u0433\u0440\u0443\u043F\u043F\u044B \u041B\u0438,\u0430\u043B\u0433\u0435\u0431\u0440\u044B \u041B\u0438 \u0438\u043B\u0438 \u0434\u0440\u0443\u0433\u0438\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u043E\u0431\u044A\u0435\u043A\u0442\u043E\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0413\u0435\u0440\u043C\u0430\u043D\u0430 \u0412\u0435\u0439\u043B\u044F."@ru . . . . "\u0413\u0440\u0443\u043F\u043F\u0430 \u0412\u0435\u0439\u043B\u044F \u2014 \u0433\u0440\u0443\u043F\u043F\u0430, \u043F\u043E\u0440\u043E\u0436\u0434\u0451\u043D\u043D\u0430\u044F \u043E\u0442\u0440\u0430\u0436\u0435\u043D\u0438\u044F\u043C\u0438 \u0432 \u0433\u0438\u043F\u0435\u0440\u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u044F\u0445, \u043E\u0440\u0442\u043E\u0433\u043E\u043D\u0430\u043B\u044C\u043D\u044B\u0445 \u043A \u043A\u043E\u0440\u043D\u044F\u043C \u043A\u043E\u0440\u043D\u0435\u0432\u043E\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u044B \u0433\u0440\u0443\u043F\u043F\u044B \u041B\u0438,\u0430\u043B\u0433\u0435\u0431\u0440\u044B \u041B\u0438 \u0438\u043B\u0438 \u0434\u0440\u0443\u0433\u0438\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u043E\u0431\u044A\u0435\u043A\u0442\u043E\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0413\u0435\u0440\u043C\u0430\u043D\u0430 \u0412\u0435\u0439\u043B\u044F."@ru . . . "1027344393"^^ . "In matematica, in particolare la teoria delle algebre di Lie, il gruppo di Weyl (dal nome di Hermann Weyl) di un sistema di radici \u00E8 un sottogruppo del gruppo di isometrie di quel sistema di radici. Nello specifico, \u00E8 il sottogruppo che si genera per riflessioni attraverso gli iperpiani ortogonali alle radici, e come tale \u00E8 un gruppo finito di riflessioni. Infatti risulta che la maggior parte dei gruppi di riflessione finiti sono gruppi di Weyl. [1] astratto, i gruppi di Weyl sono gruppi di Coxeter finiti e ne sono esempi importanti."@it . . . . "\u6570\u5B66\u3001\u7279\u306B\u30EA\u30FC\u74B0\u306E\u7406\u8AD6\u306B\u304A\u3044\u3066\u3001\u30EB\u30FC\u30C8\u7CFB \u03A6 \u306E\u30EF\u30A4\u30EB\u7FA4\uFF08\u82F1: Weyl group\uFF09\u306F\u3001\u30EB\u30FC\u30C8\u7CFB\u306E\u306E\u90E8\u5206\u7FA4\u3067\u3042\u308B\u3002\u5177\u4F53\u7684\u306B\u306F\u3001\u30EB\u30FC\u30C8\u306B\u76F4\u4EA4\u3059\u308B\u8D85\u5E73\u9762\u306B\u95A2\u3059\u308B\u93E1\u6620\u306B\u3088\u3063\u3066\u751F\u6210\u3055\u308C\u308B\u90E8\u5206\u7FA4\u306E\u3053\u3068\u3067\u3001\u305D\u306E\u3088\u3046\u306A\u3082\u306E\u3068\u3057\u3066\u3067\u3042\u308B\u3002\u62BD\u8C61\u7684\u306B\u306F\u3001\u30EF\u30A4\u30EB\u7FA4\u306F\u3067\u3042\u308A\u3001\u305D\u306E\u91CD\u8981\u306A\u4F8B\u3067\u3042\u308B\u3002 \u534A\u5358\u7D14\u30EA\u30FC\u7FA4\u3001\u534A\u5358\u7D14\u30EA\u30FC\u74B0\u3001\u7DDA\u578B\u4EE3\u6570\u7FA4\u3001\u306A\u3069\u306E\u30EF\u30A4\u30EB\u7FA4\u306F\u305D\u306E\u7FA4\u3042\u308B\u3044\u306F\u74B0\u306E\u30EB\u30FC\u30C8\u7CFB\u306E\u30EF\u30A4\u30EB\u7FA4\u3067\u3042\u308B\u3002 \u540D\u524D\u306F\u30D8\u30EB\u30DE\u30F3\u30FB\u30EF\u30A4\u30EB (Hermann Weyl) \u306B\u3061\u306A\u3080\u3002"@ja . "Grup\u0105 Weyla \u2013 grupa symetrii uk\u0142adu pierwiastkowego. W zale\u017Cno\u015Bci od konkretnej realizacji uk\u0142adu pierwiastkowego rozpatrywane s\u0105 r\u00F3\u017Cne grupy Weyla: , , grupy algebraicznej."@pl . . . . . . . . "Weyl group"@en . "Groupe de Weyl"@fr . . . "Grupo de Weyl"@es . "\u5728\u6578\u5B78\u88E1\uFF0C\u5C24\u5176\u662F\u5728\u674E\u7FA4\u7684\u7406\u8AD6\u4E2D\uFF0C\u4E00\u6839\u7CFB\u7684\u5916\u5C14\u7FA4\u662F\u6307\u7D93\u7531\u6B63\u4EA4\u65BC\u6839\u4E4B\u8D85\u5E73\u9762\u7684\u93E1\u9762\u800C\u7522\u751F\u4E4B\u6839\u7CFB\u7684\u7B49\u8DDD\u540C\u69CB\u7FA4\u4E4B\u5B50\u7FA4\u3002\u4F8B\u5982\uFF0C\u6839\u7CFBA2\u5305\u542B\u4E2D\u5FC3\u70BA\u539F\u9EDE\u4E4B\u6B63\u516D\u908A\u5F62\u7684\u89D2\u3002\u6839\u7CFB\u7684\u5C0D\u7A31\u4E4B\u6574\u500B\u7FA4\u56E0\u6B64\u662F\u670912\u968E\u7684\u4E8C\u9762\u9AD4\u7FA4\u3002\u5916\u5C14\u7FA4\u7522\u751F\u65BC\u5C07\u516D\u908A\u5F62\u5E73\u5206\u6210\u5169\u534A\u7684\u7DDA\u4E4B\u93E1\u5C04\uFF1B\u5176\u70BA6\u968E\u7684\u4E8C\u9762\u9AD4\u7FA4\u3002 \u674E\u7FA4\u3001\u534A\u55AE\u674E\u4EE3\u6578\u548C\u534A\u55AE\u7B49\u4E4B\u5916\u5C14\u7FA4\u70BA\u7FA4\u6216\u4EE3\u6578\u4E4B\u6839\u7CFB\u7684\u5916\u5C14\u7FA4\u3002 \u9664\u53BB\u7531\u03A6\u7684\u6839\u6240\u5B9A\u7FA9\u4E4B\u8D85\u5E73\u9762\u6703\u5C07\u6B50\u5E7E\u91CC\u5F97\u7A7A\u9593\u5207\u6210\u6709\u9650\u500B\u958B\u9818\u57DF\uFF0C\u6B64\u9818\u57DF\u7A31\u70BA\u5916\u5C14\u8154\u3002\u9019\u4E9B\u9818\u57DF\u53EF\u4EE5\u88AB\u5916\u5C14\u7FA4\u7684\u7FA4\u4F5C\u7528\u7F6E\u63DB\uFF0C\u4E14\u6B64\u4E00\u7FA4\u4F5C\u7528\u70BA\u7C21\u55AE\u50B3\u905E\u7684\u3002\u7279\u5225\u5730\u662F\uFF0C\u5916\u5C14\u8154\u7684\u6578\u91CF\u662F\u548C\u5916\u5C14\u7FA4\u7684\u968E\u76F8\u540C\u7684\u3002\u4EFB\u4E00\u975E\u96F6\u5411\u91CF\u90FD\u53EF\u4EE5\u4EE5\u6B63\u4EA4\u65BCv\u4E4B\u8D85\u5E73\u9762v\u2227\u5C07\u6B50\u5E7E\u91CC\u5F97\u7A7A\u9593\u5206\u6210\u5169\u500B\u534A\u7A7A\u9593\uFF0Dv+\u548Cv\u2212\u3002\u82E5v\u5728\u67D0\u4E00\u5916\u5C14\u8154\u88E1\uFF0C\u5247\u6C92\u6709\u6839\u6703\u5728v\u2227\uFF0C\u6240\u4EE5\u6BCF\u4E00\u500B\u6839\u90FD\u6703\u5728v+\u6216v\u2212\u88E1\uFF0C\u4E14\u82E5\u5176\u4E00\u6839\u03B1\u5728\u4E00\u908A\uFF0C\u5247\u5176\u53E6\u5916\u4E00\u6839\u2212\u03B1\u6703\u5728\u53E6\u5916\u4E00\u908A\u3002\u56E0\u6B64\uFF0C\u03A6+ := \u03A6\u2229v+\u5305\u542B\u8457\u03A6\u6B63\u597D\u4E00\u534A\u7684\u6839\u3002\u7576\u7136\u03A6+\u548Cv\u6709\u95DC\uFF0C\u4F46\u53EA\u8981v\u5F85\u5728\u540C\u4E00\u500B\u5916\u5C14\u8154\u88E1\uFF0C\u03A6+\u5C31\u4E0D\u6703\u6539\u8B8A\u3002\u6839\u64DA\u4E0A\u8FF0\u9078\u64C7\u7684\u6839\u7CFB\u4E4B\u57FA\u70BA\u5728\u03A6+\u5167\u7684\u7C21\u55AE\u6839\uFF0C\u5373\u5176\u4E0D\u80FD\u88AB\u5BEB\u6210\u65BC\u03A6+\u5167\u53E6\u5916\u5169\u500B\u6839\u4E4B\u548C\u7684\u6839\u3002\u56E0\u6B64\uFF0C\u5916\u5C14\u8154\u3001\u03A6+\u548C\u5176\u57FA\u6C7A\u5B9A\u4E86\u53E6\u4E00\u500B\uFF0C\u4E14\u5916\u5C14\u7FA4\u5728\u6BCF\u4E00\u72C0\u6CC1\u4E0B\u90FD\u70BA\u7C21\u55AE\u50B3\u905E\u3002\u4E0B\u9762\u7684\u5716\u793A\u63CF\u7E6A\u4E86\u6839\u7CFBA2\u7684\u516D\u500B\u5916\u5C14\u8154\uFF0C\u4E00\u9078\u5B9A\u7684v\u53CA\u5176\u8D85\u5E73\u9762v\u2227(\u4EE5\u865B\u7DDA\u8868\u793A)\u53CA\u6B63\u6839\u03B1\u3001\u03B2\u548C\u03B3\u3002\u6B64\u4F8B\u4E2D\u7684\u57FA\u70BA{\u03B1,\u03B3}\u3002 \u5916\u5C14\u7FA4\u70BA\u8003\u514B\u65AF\u7279\u7FA4\u7684\u4E00\u7279\u4F8B\u3002\u9019\u8868\u793A\u5176\u6709\u4E00\u7279\u6B8A\u7A2E\u985E\u7684\u5C55\u73FE\uFF0C\u5176\u4E2D\u6BCF\u4E00\u7522\u751F\u5B50xi\u5747\u70BA\u4E8C\u968E\uFF0C\u4E14\u6709\u7570\u65BCxi2\u7684\u95DC\u4FC2(xixj)mij\u3002\u7522\u751F\u5B50\u662F\u7531\u7C21\u55AE\u6839\u6240\u7D66\u51FA\u7684\u93E1\u5C04\uFF0C\u4E14mij\u4F9D\u64DA\u6839i\u548Cj\u4E4B\u9593\u7684\u89D2\u5EA6\u70BA90\u5EA6\u3001120\u5EA6\u3001135\u5EA6\u6216150\u5EA6\u7B49\u4E0D\u540C(\u5373\u6839\u64DA\u5176\u5728\u9127\u80AF\u5716\u5167\u70BA\u4E0D\u76F8\u9023\u3001\u4EE5\u55AE\u908A\u76F8\u9023\u3001\u4EE5\u96D9\u908A\u76F8\u9023\u3001\u4EE5\u4E09\u908A\u76F8\u9023)\u800C\u5206\u5225\u70BA2\u30013\u30014\u53CA6\u3002\u4E00\u5916\u5C14\u7FA4\u5143\u7D20\u7684\u9577\u5EA6\u70BA\u53EF\u4EE5\u4EE5\u6700\u5C11\u5B57\u5C55\u73FE\u5176\u4EE5\u6A19\u6E96\u7522\u751F\u5B50\u8868\u793A\u4E4B\u5143\u7D20\u7684\u9577\u5EA6\u3002 \u82E5G\u70BA\u4E00\u5728\u4EE3\u6578\u9589\u9AD4\u4E0A\u7684\u534A\u55AE\u7DDA\u4EE3\u6578\u7FA4\uFF0C\u4E14T\u70BA\u4E00\u6975\u5927\u74B0\u9762\uFF0C\u5247T\u7684\u6B63\u898F\u5316\u5B50N\u5305\u542B\u8457T\uFF0C\u70BA\u4E00\u6709\u9650\u6307\u6578\u4E4B\u5B50\u7FA4\uFF0C\u4E14G\u7684\u5916\u5C14\u7FA4W\u6703\u540C\u69CB\u65BCN/T\u3002\u82E5B\u70BAG\u7684\u4E14\u5C07T\u9078\u5B9A\u653E\u5728B\u5167\uFF0C\u5373\u53EF\u5F97\u5230\u5E03\u5415\u963F\u5206\u89E3 \u5176\u5C07G/B\u7684\u5206\u89E3\u6620\u5C04\u81F3\u8212\u4F2F\u7279\u7D30\u80DE\u5167\u3002(\u8A73\u898B\u683C\u62C9\u65AF\u66FC\u7A7A\u9593)"@zh . . . . . "\u0413\u0440\u0443\u043F\u0430 \u0412\u0435\u0439\u043B\u044F \u2014 \u0433\u0440\u0443\u043F\u0430, \u043F\u043E\u0440\u043E\u0434\u0436\u0435\u043D\u0430 \u0432\u0456\u0434\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u043D\u044F\u043C\u0438 \u0432 \u0433\u0456\u043F\u0435\u0440\u043F\u043B\u043E\u0449\u0438\u043D\u0430\u043C\u0438, \u043E\u0440\u0442\u043E\u0433\u043E\u043D\u0430\u043B\u044C\u043D\u0438\u043C\u0438 \u0434\u043E \u043A\u043E\u0440\u0435\u043D\u0456\u0432 \u043A\u043E\u0440\u0435\u043D\u0435\u0432\u043E\u0457 \u0441\u0438\u0441\u0442\u0435\u043C\u0438 \u0433\u0440\u0443\u043F\u0438 \u041B\u0456, \u0430\u043B\u0433\u0435\u0431\u0440\u0438 \u041B\u0456 \u0430\u0431\u043E \u0456\u043D\u0448\u0438\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0438\u0445 \u043E\u0431'\u0454\u043A\u0442\u0456\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0413\u0435\u0440\u043C\u0430\u043D\u0430 \u0412\u0435\u0439\u043B\u044F."@uk . "Gruppo di Weyl"@it . . "\u0413\u0440\u0443\u043F\u0430 \u0412\u0435\u0439\u043B\u044F \u2014 \u0433\u0440\u0443\u043F\u0430, \u043F\u043E\u0440\u043E\u0434\u0436\u0435\u043D\u0430 \u0432\u0456\u0434\u043E\u0431\u0440\u0430\u0436\u0435\u043D\u043D\u044F\u043C\u0438 \u0432 \u0433\u0456\u043F\u0435\u0440\u043F\u043B\u043E\u0449\u0438\u043D\u0430\u043C\u0438, \u043E\u0440\u0442\u043E\u0433\u043E\u043D\u0430\u043B\u044C\u043D\u0438\u043C\u0438 \u0434\u043E \u043A\u043E\u0440\u0435\u043D\u0456\u0432 \u043A\u043E\u0440\u0435\u043D\u0435\u0432\u043E\u0457 \u0441\u0438\u0441\u0442\u0435\u043C\u0438 \u0433\u0440\u0443\u043F\u0438 \u041B\u0456, \u0430\u043B\u0433\u0435\u0431\u0440\u0438 \u041B\u0456 \u0430\u0431\u043E \u0456\u043D\u0448\u0438\u0445 \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0438\u0445 \u043E\u0431'\u0454\u043A\u0442\u0456\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0413\u0435\u0440\u043C\u0430\u043D\u0430 \u0412\u0435\u0439\u043B\u044F."@uk . . . . . "In de groepentheorie, een deelgebied van de wiskunde, en met name in de theorie van de Lie-algebra's, is de weyl-groep van een wortelsysteem, , een deelgroep van de isometriegroep van dat wortelsysteem. Concreet is het de deelgroep die wordt gegenereerd door spiegelingen door de hypervlakken die loodrecht op de wortels staan. Het wortelstelsel van bijvoorbeeld bestaat uit de hoekpunten van een regelmatige zeshoek die in de oorsprong is gecentreerd. De weyl-groep van dit wortelsysteem is een deelgroep van index twee van de dihedrale groep van orde 12. De weyl-groep is isomorf met , de symmetrische groep, die wordt gegenereerd door de drie spiegelingen op de hoofddiagonaal van de zeshoek. De weyl-groep van een halfenkelvoudige lie-groep, een halfenkelvoudige lie-algebra, een halfenkelvoudige , enz. is de weyl-groep van het wortelstelsel van die groep of die algebra"@nl . . "\u5728\u6578\u5B78\u88E1\uFF0C\u5C24\u5176\u662F\u5728\u674E\u7FA4\u7684\u7406\u8AD6\u4E2D\uFF0C\u4E00\u6839\u7CFB\u7684\u5916\u5C14\u7FA4\u662F\u6307\u7D93\u7531\u6B63\u4EA4\u65BC\u6839\u4E4B\u8D85\u5E73\u9762\u7684\u93E1\u9762\u800C\u7522\u751F\u4E4B\u6839\u7CFB\u7684\u7B49\u8DDD\u540C\u69CB\u7FA4\u4E4B\u5B50\u7FA4\u3002\u4F8B\u5982\uFF0C\u6839\u7CFBA2\u5305\u542B\u4E2D\u5FC3\u70BA\u539F\u9EDE\u4E4B\u6B63\u516D\u908A\u5F62\u7684\u89D2\u3002\u6839\u7CFB\u7684\u5C0D\u7A31\u4E4B\u6574\u500B\u7FA4\u56E0\u6B64\u662F\u670912\u968E\u7684\u4E8C\u9762\u9AD4\u7FA4\u3002\u5916\u5C14\u7FA4\u7522\u751F\u65BC\u5C07\u516D\u908A\u5F62\u5E73\u5206\u6210\u5169\u534A\u7684\u7DDA\u4E4B\u93E1\u5C04\uFF1B\u5176\u70BA6\u968E\u7684\u4E8C\u9762\u9AD4\u7FA4\u3002 \u674E\u7FA4\u3001\u534A\u55AE\u674E\u4EE3\u6578\u548C\u534A\u55AE\u7B49\u4E4B\u5916\u5C14\u7FA4\u70BA\u7FA4\u6216\u4EE3\u6578\u4E4B\u6839\u7CFB\u7684\u5916\u5C14\u7FA4\u3002 \u9664\u53BB\u7531\u03A6\u7684\u6839\u6240\u5B9A\u7FA9\u4E4B\u8D85\u5E73\u9762\u6703\u5C07\u6B50\u5E7E\u91CC\u5F97\u7A7A\u9593\u5207\u6210\u6709\u9650\u500B\u958B\u9818\u57DF\uFF0C\u6B64\u9818\u57DF\u7A31\u70BA\u5916\u5C14\u8154\u3002\u9019\u4E9B\u9818\u57DF\u53EF\u4EE5\u88AB\u5916\u5C14\u7FA4\u7684\u7FA4\u4F5C\u7528\u7F6E\u63DB\uFF0C\u4E14\u6B64\u4E00\u7FA4\u4F5C\u7528\u70BA\u7C21\u55AE\u50B3\u905E\u7684\u3002\u7279\u5225\u5730\u662F\uFF0C\u5916\u5C14\u8154\u7684\u6578\u91CF\u662F\u548C\u5916\u5C14\u7FA4\u7684\u968E\u76F8\u540C\u7684\u3002\u4EFB\u4E00\u975E\u96F6\u5411\u91CF\u90FD\u53EF\u4EE5\u4EE5\u6B63\u4EA4\u65BCv\u4E4B\u8D85\u5E73\u9762v\u2227\u5C07\u6B50\u5E7E\u91CC\u5F97\u7A7A\u9593\u5206\u6210\u5169\u500B\u534A\u7A7A\u9593\uFF0Dv+\u548Cv\u2212\u3002\u82E5v\u5728\u67D0\u4E00\u5916\u5C14\u8154\u88E1\uFF0C\u5247\u6C92\u6709\u6839\u6703\u5728v\u2227\uFF0C\u6240\u4EE5\u6BCF\u4E00\u500B\u6839\u90FD\u6703\u5728v+\u6216v\u2212\u88E1\uFF0C\u4E14\u82E5\u5176\u4E00\u6839\u03B1\u5728\u4E00\u908A\uFF0C\u5247\u5176\u53E6\u5916\u4E00\u6839\u2212\u03B1\u6703\u5728\u53E6\u5916\u4E00\u908A\u3002\u56E0\u6B64\uFF0C\u03A6+ := \u03A6\u2229v+\u5305\u542B\u8457\u03A6\u6B63\u597D\u4E00\u534A\u7684\u6839\u3002\u7576\u7136\u03A6+\u548Cv\u6709\u95DC\uFF0C\u4F46\u53EA\u8981v\u5F85\u5728\u540C\u4E00\u500B\u5916\u5C14\u8154\u88E1\uFF0C\u03A6+\u5C31\u4E0D\u6703\u6539\u8B8A\u3002\u6839\u64DA\u4E0A\u8FF0\u9078\u64C7\u7684\u6839\u7CFB\u4E4B\u57FA\u70BA\u5728\u03A6+\u5167\u7684\u7C21\u55AE\u6839\uFF0C\u5373\u5176\u4E0D\u80FD\u88AB\u5BEB\u6210\u65BC\u03A6+\u5167\u53E6\u5916\u5169\u500B\u6839\u4E4B\u548C\u7684\u6839\u3002\u56E0\u6B64\uFF0C\u5916\u5C14\u8154\u3001\u03A6+\u548C\u5176\u57FA\u6C7A\u5B9A\u4E86\u53E6\u4E00\u500B\uFF0C\u4E14\u5916\u5C14\u7FA4\u5728\u6BCF\u4E00\u72C0\u6CC1\u4E0B\u90FD\u70BA\u7C21\u55AE\u50B3\u905E\u3002\u4E0B\u9762\u7684\u5716\u793A\u63CF\u7E6A\u4E86\u6839\u7CFBA2\u7684\u516D\u500B\u5916\u5C14\u8154\uFF0C\u4E00\u9078\u5B9A\u7684v\u53CA\u5176\u8D85\u5E73\u9762v\u2227(\u4EE5\u865B\u7DDA\u8868\u793A)\u53CA\u6B63\u6839\u03B1\u3001\u03B2\u548C\u03B3\u3002\u6B64\u4F8B\u4E2D\u7684\u57FA\u70BA{\u03B1,\u03B3}\u3002 \u5176\u5C07G/B\u7684\u5206\u89E3\u6620\u5C04\u81F3\u8212\u4F2F\u7279\u7D30\u80DE\u5167\u3002(\u8A73\u898B\u683C\u62C9\u65AF\u66FC\u7A7A\u9593)"@zh . . . . "Grup\u0105 Weyla \u2013 grupa symetrii uk\u0142adu pierwiastkowego. W zale\u017Cno\u015Bci od konkretnej realizacji uk\u0142adu pierwiastkowego rozpatrywane s\u0105 r\u00F3\u017Cne grupy Weyla: , , grupy algebraicznej."@pl . . . "\u0413\u0440\u0443\u043F\u0430 \u0412\u0435\u0439\u043B\u044F"@uk . . . "En math\u00E9matiques, et en particulier dans la th\u00E9orie des alg\u00E8bres de Lie, le groupe de Weyl d'un syst\u00E8me de racines , nomm\u00E9 ainsi en hommage \u00E0 Hermann Weyl, est le sous-groupe du groupe d'isom\u00E9tries du syst\u00E8me de racines engendr\u00E9 par les r\u00E9flexions orthogonales par rapport aux hyperplans orthogonaux aux racines."@fr . "Vladimir L. Popov"@en . . "Weyl group"@en . . . . . . . .