<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://zh.dbpedia.org/resource/\u5609\u5F53\u5B50\u4EE3\u6570> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#label>	"\u041F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u0430\u0440\u0442\u0430\u043D\u0430"@ru .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#comment>	"In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra of a Lie algebra that is self-normalising (if for all , then ). They were introduced by \u00C9lie Cartan in his doctoral thesis. It controls the representation theory of a semi-simple Lie algebra over a field of characteristic . Kac\u2013Moody algebras and generalized Kac\u2013Moody algebras also have subalgebras that play the same role as the Cartan subalgebras of semisimple Lie algebras (over a field of characteristic zero)."@en .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://uk.dbpedia.org/resource/\u041F\u0456\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430_\u041A\u0430\u0440\u0442\u0430\u043D\u0430> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://ko.dbpedia.org/resource/\uCE74\uB974\uD0D5_\uBD80\uBD84_\uB300\uC218> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Regular_element_of_a_Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Identity_component> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Clarify> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456, \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u0442\u0435\u043E\u0440\u0456\u0457 \u0430\u043B\u0433\u0435\u0431\u0440 \u041B\u0456, \u043F\u0456\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430\u043C\u0438 \u041A\u0430\u0440\u0442\u0430\u043D\u0430 \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C\u0441\u044F \u043F\u0435\u0432\u043D\u0456 \u043D\u0456\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u0456 \u043F\u0456\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0438, \u044F\u043A\u0456 \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u043C\u0430\u044E\u0442\u044C \u0432\u0435\u043B\u0438\u043A\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0434\u043B\u044F \u043A\u043B\u0430\u0441\u0438\u0444\u0456\u043A\u0430\u0446\u0456\u0457 \u043D\u0430\u043F\u0456\u0432\u043F\u0440\u043E\u0441\u0442\u0438\u0445 \u0430\u043B\u0433\u0435\u0431\u0440 \u041B\u0456 \u0456 \u0432 \u0442\u0435\u043E\u0440\u0456\u0457 \u0441\u0438\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0456 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0415\u043B\u0456 \u041A\u0430\u0440\u0442\u0430\u043D\u0430."@uk .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Self-normalising> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Diagonalizable_matrix> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Science105999797> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Main> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#label>	"\u5609\u5F53\u5B50\u4EE3\u6570"@zh .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#label>	"\u041F\u0456\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u0430\u0440\u0442\u0430\u043D\u0430"@uk .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/abstract>	"\u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456, \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u0442\u0435\u043E\u0440\u0456\u0457 \u0430\u043B\u0433\u0435\u0431\u0440 \u041B\u0456, \u043F\u0456\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430\u043C\u0438 \u041A\u0430\u0440\u0442\u0430\u043D\u0430 \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C\u0441\u044F \u043F\u0435\u0432\u043D\u0456 \u043D\u0456\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u0456 \u043F\u0456\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0438, \u044F\u043A\u0456 \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u043C\u0430\u044E\u0442\u044C \u0432\u0435\u043B\u0438\u043A\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0434\u043B\u044F \u043A\u043B\u0430\u0441\u0438\u0444\u0456\u043A\u0430\u0446\u0456\u0457 \u043D\u0430\u043F\u0456\u0432\u043F\u0440\u043E\u0441\u0442\u0438\u0445 \u0430\u043B\u0433\u0435\u0431\u0440 \u041B\u0456 \u0456 \u0432 \u0442\u0435\u043E\u0440\u0456\u0457 \u0441\u0438\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0456 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0415\u043B\u0456 \u041A\u0430\u0440\u0442\u0430\u043D\u0430."@uk .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Fact> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Kac\u2013Moody_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageExternalLink>	<https://web.archive.org/web/20191029165616/http:/pi.math.cornell.edu/~dmehrle/notes/partiii/liealg_partiii_notes.pdf> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Generalized_Kac\u2013Moody_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#seeAlso>	<http://dbpedia.org/resource/Semisimple_Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://ja.dbpedia.org/resource/\u30AB\u30EB\u30BF\u30F3\u90E8\u5206\u74B0> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<https://global.dbpedia.org/id/2hknK> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/WikicatLieAlgebras> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Discipline105996646> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/abstract>	"\u5728\u6570\u5B66\u4E2D\uFF0C\u5609\u5F53\u5B50\u4EE3\u6570\uFF08Cartan subalgebra\uFF0C\u7F29\u5199\u4E3A CSA\uFF09\uFF0C\u662F\u4E00\u4E2A\u674E\u4EE3\u6570 \u7684\u81EA\u6B63\u89C4\u5316\uFF08\u5982\u679C \u5BF9\u6240\u6709 \uFF0C\u90A3\u4E48\uFF09\u3001\u5E42\u96F6\u5B50\u4EE3\u6570\uFF0C\u901A\u5E38\u7528 \u8868\u793A\u3002"@zh .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/PsychologicalFeature100023100> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Weyl_group> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u041F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u0430\u0440\u0442\u0430\u043D\u0430 \u2014 \u043F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430 \u041B\u0438 , \u0440\u0430\u0432\u043D\u0430\u044F \u0441\u0432\u043E\u0435\u043C\u0443 \u043D\u043E\u0440\u043C\u0430\u043B\u0438\u0437\u0430\u0442\u043E\u0440\u0443: \n* \u0434\u043B\u044F \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u043E\u0433\u043E (\u043D\u0438\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u043E\u0441\u0442\u044C), \n* (\u0441\u0430\u043C\u043E\u043D\u043E\u0440\u043C\u0430\u043B\u0438\u0437\u043E\u0432\u0430\u043D\u043D\u043E\u0441\u0442\u044C). \u041F\u043E\u043D\u044F\u0442\u0438\u0435 \u0438\u043C\u0435\u0435\u0442 \u0431\u043E\u043B\u044C\u0448\u043E\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u0435 \u0434\u043B\u044F \u043A\u043B\u0430\u0441\u0441\u0438\u0444\u0438\u043A\u0430\u0446\u0438\u0438 \u043F\u043E\u043B\u0443\u043F\u0440\u043E\u0441\u0442\u044B\u0445 \u0430\u043B\u0433\u0435\u0431\u0440 \u041B\u0438 \u0438 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0441\u0438\u043C\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u044B\u0445 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u042D\u043B\u0438 \u041A\u0430\u0440\u0442\u0430\u043D\u0430. \u042D\u043A\u0432\u0438\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435: \u043D\u0438\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u0430\u044F \u043F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u043E\u0439 \u041A\u0430\u0440\u0442\u0430\u043D\u0430, \u0435\u0441\u043B\u0438 \u043E\u043D\u0430 \u0440\u0430\u0432\u043D\u0430 \u0441\u0432\u043E\u0435\u0439 \u043D\u0443\u043B\u044C-\u043A\u043E\u043C\u043F\u043E\u043D\u0435\u043D\u0442\u0435 \u0424\u0438\u0442\u0442\u0438\u043D\u0433\u0430, \u0442\u043E \u0435\u0441\u0442\u044C \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0443: \u0433\u0434\u0435 \u2014 \u043F\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 .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/KnowledgeDomain105999266> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://purl.org/dc/terms/subject>	<http://dbpedia.org/resource/Category:Lie_algebras> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#comment>	"In der Mathematik, speziell in der Theorie der Lie-Algebren, werden Cartan-Unteralgebren unter anderem in der Klassifikation der halbeinfachen Lie-Algebren und in der Theorie der symmetrischen R\u00E4ume verwendet. Der Rang einer Lie-Algebra (oder der zugeh\u00F6rigen Lie-Gruppe) ist definiert als die Dimension der Cartan-Unteralgebra. Ein Beispiel einer Cartan-Unteralgebra ist die Algebra der Diagonalmatrizen."@de .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\uB9AC \uB300\uC218 \uC774\uB860\uC5D0\uC11C, \uCE74\uB974\uD0D5 \uBD80\uBD84 \uB300\uC218(Cartan\u90E8\u5206\u4EE3\u6578, \uC601\uC5B4: Cartan subalgebra)\uB294 \uB9AC \uB300\uC218\uC758 \uCD5C\uB300 \uC544\uBCA8 \uBD80\uBD84 \uB300\uC218\uC758 \uC77C\uC885\uC774\uB2E4."@ko .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Category:Lie_algebras> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://xmlns.com/foaf/0.1/isPrimaryTopicOf>	<http://en.wikipedia.org/wiki/Cartan_subalgebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#label>	"Cartan subalgebra"@en .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageExternalLink>	<https://archive.org/details/introductiontoli00jame> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Toral_subalgebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/last>	"Popov"@en .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageLength>	"14377"^^<http://www.w3.org/2001/XMLSchema#nonNegativeInteger> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Graduate_Texts_in_Mathematics> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Nilpotent_Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/abstract>	"\uB9AC \uB300\uC218 \uC774\uB860\uC5D0\uC11C, \uCE74\uB974\uD0D5 \uBD80\uBD84 \uB300\uC218(Cartan\u90E8\u5206\u4EE3\u6578, \uC601\uC5B4: Cartan subalgebra)\uB294 \uB9AC \uB300\uC218\uC758 \uCD5C\uB300 \uC544\uBCA8 \uBD80\uBD84 \uB300\uC218\uC758 \uC77C\uC885\uC774\uB2E4."@ko .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Adjoint_representation_of_a_Lie_group> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Representation_theory_of_semisimple_Lie_algebras> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Content105809192> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Abstraction100002137> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#label>	"\u30AB\u30EB\u30BF\u30F3\u90E8\u5206\u74B0"@ja .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/David_Vogan> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Fundamental_Weyl_chamber> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#label>	"Cartan-Unteralgebra"@de .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Mathematics> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:See_also> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://www.wikidata.org/entity/Q2912114> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Lie_algebra_representation> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Centralizer> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Toral_Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/abstract>	"\u6570\u5B66\u306B\u304A\u3044\u3066\uFF0C\u30AB\u30EB\u30BF\u30F3\u90E8\u5206\u74B0\uFF08\u30AB\u30EB\u30BF\u30F3\u3076\u3076\u3093\u304B\u3093\uFF0C\u82F1: Cartan subalgebra\uFF0C\u3057\u3070\u3057\u3070 CSA \u3068\u7565\u3055\u308C\u308B\uFF09\u3068\u306F\uFF0C\u30EA\u30FC\u74B0 \u306E\u51AA\u96F6\u90E8\u5206\u74B0 \u3067\u3042\u3063\u3066\uFF0C\u306A\u3082\u306E\uFF08\u3059\u3079\u3066\u306E \u306B\u5BFE\u3057\u3066 \u3067\u3042\u308B\u306A\u3089\u3070\uFF0C \u3067\u3042\u308B\u3082\u306E\uFF09\u306E\u3053\u3068\u3067\u3042\u308B\uFF0E\u30A8\u30EA\u30FB\u30AB\u30EB\u30BF\u30F3\u306B\u3088\u3063\u3066\u5F7C\u306E\u535A\u58EB\u8AD6\u6587\u306B\u304A\u3044\u3066\u5C0E\u5165\u3055\u308C\u305F\uFF0E"@ja .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u6570\u5B66\u306B\u304A\u3044\u3066\uFF0C\u30AB\u30EB\u30BF\u30F3\u90E8\u5206\u74B0\uFF08\u30AB\u30EB\u30BF\u30F3\u3076\u3076\u3093\u304B\u3093\uFF0C\u82F1: Cartan subalgebra\uFF0C\u3057\u3070\u3057\u3070 CSA \u3068\u7565\u3055\u308C\u308B\uFF09\u3068\u306F\uFF0C\u30EA\u30FC\u74B0 \u306E\u51AA\u96F6\u90E8\u5206\u74B0 \u3067\u3042\u3063\u3066\uFF0C\u306A\u3082\u306E\uFF08\u3059\u3079\u3066\u306E \u306B\u5BFE\u3057\u3066 \u3067\u3042\u308B\u306A\u3089\u3070\uFF0C \u3067\u3042\u308B\u3082\u306E\uFF09\u306E\u3053\u3068\u3067\u3042\u308B\uFF0E\u30A8\u30EA\u30FB\u30AB\u30EB\u30BF\u30F3\u306B\u3088\u3063\u3066\u5F7C\u306E\u535A\u58EB\u8AD6\u6587\u306B\u304A\u3044\u3066\u5C0E\u5165\u3055\u308C\u305F\uFF0E"@ja .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Lie_group> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageExternalLink>	<https://web.archive.org/web/20201006224222/https:/www.maths.ed.ac.uk/~igordon/LA1.pdf> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Footnotes> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Root_system> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/first>	"V.L."@en .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageID>	"1336000"^^<http://www.w3.org/2001/XMLSchema#integer> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Abelian_Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/title>	"Cartan subalgebra"@en .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Short_description> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Split_Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Linear_Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Isomorphism> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Citation> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/PureMathematics106003682> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://ru.dbpedia.org/resource/\u041F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430_\u041A\u0430\u0440\u0442\u0430\u043D\u0430> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Automorphism> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Rank_of_a_Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Semisimple_operator> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Lie_groups> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/\u00C9lie_Cartan> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Dover_Publications> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Eom> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Mathematics106000644> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Cite_book> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/authorlink>	"Vladimir L. Popov"@en .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Semisimple_Lie_algebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/abstract>	"In der Mathematik, speziell in der Theorie der Lie-Algebren, werden Cartan-Unteralgebren unter anderem in der Klassifikation der halbeinfachen Lie-Algebren und in der Theorie der symmetrischen R\u00E4ume verwendet. Der Rang einer Lie-Algebra (oder der zugeh\u00F6rigen Lie-Gruppe) ist definiert als die Dimension der Cartan-Unteralgebra. Ein Beispiel einer Cartan-Unteralgebra ist die Algebra der Diagonalmatrizen."@de .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Splitting_Cartan_subalgebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Field_(mathematics)> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Algebra106012726> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/abstract>	"\u041F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430 \u041A\u0430\u0440\u0442\u0430\u043D\u0430 \u2014 \u043F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430 \u041B\u0438 , \u0440\u0430\u0432\u043D\u0430\u044F \u0441\u0432\u043E\u0435\u043C\u0443 \u043D\u043E\u0440\u043C\u0430\u043B\u0438\u0437\u0430\u0442\u043E\u0440\u0443: \n* \u0434\u043B\u044F \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u043E\u0433\u043E (\u043D\u0438\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u043E\u0441\u0442\u044C), \n* (\u0441\u0430\u043C\u043E\u043D\u043E\u0440\u043C\u0430\u043B\u0438\u0437\u043E\u0432\u0430\u043D\u043D\u043E\u0441\u0442\u044C). \u041F\u043E\u043D\u044F\u0442\u0438\u0435 \u0438\u043C\u0435\u0435\u0442 \u0431\u043E\u043B\u044C\u0448\u043E\u0435 \u0437\u043D\u0430\u0447\u0435\u043D\u0438\u0435 \u0434\u043B\u044F \u043A\u043B\u0430\u0441\u0441\u0438\u0444\u0438\u043A\u0430\u0446\u0438\u0438 \u043F\u043E\u043B\u0443\u043F\u0440\u043E\u0441\u0442\u044B\u0445 \u0430\u043B\u0433\u0435\u0431\u0440 \u041B\u0438 \u0438 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0441\u0438\u043C\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u044B\u0445 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u042D\u043B\u0438 \u041A\u0430\u0440\u0442\u0430\u043D\u0430. \u042D\u043A\u0432\u0438\u0432\u0430\u043B\u0435\u043D\u0442\u043D\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435: \u043D\u0438\u043B\u044C\u043F\u043E\u0442\u0435\u043D\u0442\u043D\u0430\u044F \u043F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u0430 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043F\u043E\u0434\u0430\u043B\u0433\u0435\u0431\u0440\u043E\u0439 \u041A\u0430\u0440\u0442\u0430\u043D\u0430, \u0435\u0441\u043B\u0438 \u043E\u043D\u0430 \u0440\u0430\u0432\u043D\u0430 \u0441\u0432\u043E\u0435\u0439 \u043D\u0443\u043B\u044C-\u043A\u043E\u043C\u043F\u043E\u043D\u0435\u043D\u0442\u0435 \u0424\u0438\u0442\u0442\u0438\u043D\u0433\u0430, \u0442\u043E \u0435\u0441\u0442\u044C \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0443: \u0433\u0434\u0435 \u2014 \u043F\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 .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#comment>	"\u5728\u6570\u5B66\u4E2D\uFF0C\u5609\u5F53\u5B50\u4EE3\u6570\uFF08Cartan subalgebra\uFF0C\u7F29\u5199\u4E3A CSA\uFF09\uFF0C\u662F\u4E00\u4E2A\u674E\u4EE3\u6570 \u7684\u81EA\u6B63\u89C4\u5316\uFF08\u5982\u679C \u5BF9\u6240\u6709 \uFF0C\u90A3\u4E48\uFF09\u3001\u5E42\u96F6\u5B50\u4EE3\u6570\uFF0C\u901A\u5E38\u7528 \u8868\u793A\u3002"@zh .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:Expand-section> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Springer-Verlag> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/ns/prov#wasDerivedFrom>	<http://en.wikipedia.org/wiki/Cartan_subalgebra?oldid=1117754196&ns=0> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Algebraically_closed_field> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Maximal_torus> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://he.dbpedia.org/resource/\u05EA\u05EA-\u05D0\u05DC\u05D2\u05D1\u05E8\u05EA_\u05E7\u05E8\u05D8\u05DF> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Subalgebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://rdf.freebase.com/ns/m.04tq1y> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageRevisionID>	"1117754196"^^<http://www.w3.org/2001/XMLSchema#integer> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Adjoint_endomorphism> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/property/wikiPageUsesTemplate>	<http://dbpedia.org/resource/Template:For> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://de.dbpedia.org/resource/Cartan-Unteralgebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2000/01/rdf-schema#label>	"\uCE74\uB974\uD0D5 \uBD80\uBD84 \uB300\uC218"@ko .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Square_matrix> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/2002/07/owl#sameAs>	<http://yago-knowledge.org/resource/Cartan_subalgebra> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://www.w3.org/2002/07/owl#Thing> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/abstract>	"In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra of a Lie algebra that is self-normalising (if for all , then ). They were introduced by \u00C9lie Cartan in his doctoral thesis. It controls the representation theory of a semi-simple Lie algebra over a field of characteristic . In a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero (e.g., ), a Cartan subalgebra is the same thing as a maximal abelian subalgebra consisting of elements x such that the adjoint endomorphism is semisimple (i.e., diagonalizable). Sometimes this characterization is simply taken as the definition of a Cartan subalgebra.pg 231 In general, a subalgebra is called toral if it consists of semisimple elements. Over an algebraically closed field, a toral subalgebra is automatically abelian. Thus, over an algebraically closed field of characteristic zero, a Cartan subalgebra can also be defined as a maximal toral subalgebra. Kac\u2013Moody algebras and generalized Kac\u2013Moody algebras also have subalgebras that play the same role as the Cartan subalgebras of semisimple Lie algebras (over a field of characteristic zero)."@en .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>	<http://dbpedia.org/class/yago/Cognition100023271> .
<http://dbpedia.org/resource/Cartan_subalgebra>	<http://dbpedia.org/ontology/wikiPageWikiLink>	<http://dbpedia.org/resource/Harish-Chandra_isomorphism> .