| dbo:abstract |
In mathematics, the Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to the 1880s work of Élie Cartan and Wilhelm Killing. (en) En mathématiques, la décomposition de Cartan d'un groupe de Lie ou d'une algèbre de Lie semi-simple joue un rôle important dans l'étude de leur structure et de leurs représentations. Elle généralise la décomposition polaire du groupe linéaire. (fr) 리 군론에서 카르탕 대합(Cartan對合, 영어: Cartan involution)은 킬링 형식을 음의 정부호로 만드는 리 대수 대합이다. (ko) |
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dbr:Representation_theory dbr:Totally_geodesic dbr:Lie_group dbc:Lie_algebras dbr:Compact_Lie_group dbr:Complexification dbr:SU(n) dbr:Lie_algebra dbr:Analytic_subgroup dbr:Singular_value_decomposition dbr:Élie_Cartan dbr:Automorphism dbr:Wilhelm_Killing dbc:Lie_groups dbr:Diffeomorphism dbr:Complex_conjugation dbr:Involution_(mathematics) dbr:Killing_form dbr:Polar_decomposition dbr:Positive_definite_bilinear_form dbr:Special_unitary_group dbr:Inner_automorphism dbr:Cartan_pair dbr:Semisimple_Lie_algebra dbr:Lie_group_decompositions |
| dbp:date |
October 2020 (en) |
| dbp:reason |
The very first comment on the talk page points out that the Killing form definition of the Cartan involution doesn't work for gl, so what is going on, here? How'd you get this? This is also inconsistent with the analytic-group comment on the talk page (en) Very first talk page section points out that the Killing-form definition won't work for GL. A later talk-page section points out that the transpose won't work for the analytic-subgroup claims above. So, for GL, is "any old involution" a Cartan involution? See "Inconsistency!" on talk page. (en) |
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| gold:hypernym |
dbr:Decomposition |
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| rdfs:comment |
In mathematics, the Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to the 1880s work of Élie Cartan and Wilhelm Killing. (en) En mathématiques, la décomposition de Cartan d'un groupe de Lie ou d'une algèbre de Lie semi-simple joue un rôle important dans l'étude de leur structure et de leurs représentations. Elle généralise la décomposition polaire du groupe linéaire. (fr) 리 군론에서 카르탕 대합(Cartan對合, 영어: Cartan involution)은 킬링 형식을 음의 정부호로 만드는 리 대수 대합이다. (ko) |
| rdfs:label |
Cartan-Zerlegung (de) Cartan decomposition (en) Décomposition de Cartan (fr) 카르탕 대합 (ko) |
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freebase:Cartan decomposition yago-res:Cartan decomposition wikidata:Cartan decomposition dbpedia-de:Cartan decomposition dbpedia-fr:Cartan decomposition dbpedia-ko:Cartan decomposition https://global.dbpedia.org/id/2pYNw |
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