| dbo:abstract |
In the mathematical study of Lie algebras and Lie groups, a Satake diagram is a generalization of a Dynkin diagram introduced by Satake whose configurations classify simple Lie algebras over the field of real numbers. The Satake diagrams associated to a Dynkin diagram classify real forms of the complex Lie algebra corresponding to the Dynkin diagram. More generally, the Tits index or Satake–Tits diagram of a reductive algebraic group over a field is a generalization of the Satake diagram to arbitrary fields, introduced by Tits, that reduces the classification of reductive algebraic groups to that of anisotropic reductive algebraic groups. Satake diagrams are not the same as Vogan diagrams of a Lie group, although they look similar. (en) 군론에서 사타케 도표(영어: Satake diagram)는 반단순 리 군 또는 가약군의 구조를 나타내는 그래프의 일종이다. 딘킨 도표에 추가로 꼭짓점의 색깔(검은색 또는 흰색)과 흰 꼭짓점 위의 절대 갈루아 군의 작용을 그린 것이다. (ko) |
| dbo:wikiPageExternalLink |
https://books.google.com/books%3Fid=HQbvAAAAMAAJ https://books.google.com/books%3Fid=l8nJCNiIQAAC%7Cpublisher=Springer https://books.google.com/books%3Fid=l8nJCNiIQAAC&pg=PA229 http://relativity.livingreviews.org/open%3FpubNo=lrr-2008-1&page=articlesu39.html http://resolver.sub.uni-goettingen.de/purl%3FGDZPPN002185725 |
| dbo:wikiPageID |
20514575 (xsd:integer) |
| dbo:wikiPageLength |
7044 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1109823173 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Algebraic_group dbr:Annals_of_Mathematics dbr:Dynkin_diagram dbr:Lie_group dbr:List_of_irreducible_Tits_indices dbc:Lie_algebras dbr:Mathematics dbr:Lie_algebra dbr:Compact_Lie_algebra dbr:Galois_cohomology dbr:Linear_algebraic_group dbr:American_Mathematical_Society dbr:Field_(mathematics) dbr:Graduate_Studies_in_Mathematics dbr:Reductive_group dbr:Cartan_decomposition dbr:Cartan_subalgebra dbr:Real_number dbr:Semisimple_Lie_algebra dbr:Vogan_diagram dbr:Real_form_(Lie_theory) dbr:Split_Lie_algebra dbr:Springer-Verlag dbr:Journal_für_die_reine_und_angewandte_Mathematik dbr:Relative_root_system |
| dbp:authorlink |
Ichirô Satake (en) |
| dbp:last |
Satake (en) |
| dbp:loc |
p.109 (en) |
| dbp:wikiPageUsesTemplate |
dbt:Citation dbt:Expand_section dbt:Harv dbt:Harvs |
| dbp:year |
1960 (xsd:integer) |
| dcterms:subject |
dbc:Lie_algebras |
| gold:hypernym |
dbr:Generalization |
| rdf:type |
yago:WikicatLieAlgebras yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:Science105999797 |
| rdfs:comment |
군론에서 사타케 도표(영어: Satake diagram)는 반단순 리 군 또는 가약군의 구조를 나타내는 그래프의 일종이다. 딘킨 도표에 추가로 꼭짓점의 색깔(검은색 또는 흰색)과 흰 꼭짓점 위의 절대 갈루아 군의 작용을 그린 것이다. (ko) In the mathematical study of Lie algebras and Lie groups, a Satake diagram is a generalization of a Dynkin diagram introduced by Satake whose configurations classify simple Lie algebras over the field of real numbers. The Satake diagrams associated to a Dynkin diagram classify real forms of the complex Lie algebra corresponding to the Dynkin diagram. Satake diagrams are not the same as Vogan diagrams of a Lie group, although they look similar. (en) |
| rdfs:label |
사타케 도표 (ko) Satake diagram (en) |
| owl:sameAs |
freebase:Satake diagram yago-res:Satake diagram wikidata:Satake diagram dbpedia-ko:Satake diagram https://global.dbpedia.org/id/4v96S |
| prov:wasDerivedFrom |
wikipedia-en:Satake_diagram?oldid=1109823173&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Satake_diagram |
| is dbo:knownFor of |
dbr:Ichirō_Satake |
| is dbo:wikiPageDisambiguates of |
dbr:Satake |
| is dbo:wikiPageRedirects of |
dbr:Tits-Satake_diagram dbr:Tits_index dbr:Tits–Satake_diagram |
| is dbo:wikiPageWikiLink of |
dbr:Dynkin_diagram dbr:Compact_Lie_algebra dbr:Symmetric_space dbr:Linear_algebraic_group dbr:Simple_Lie_group dbr:Reductive_group dbr:Ichirō_Satake dbr:Satake dbr:Restricted_root_system dbr:Semisimple_Lie_algebra dbr:Vogan_diagram dbr:Real_form_(Lie_theory) dbr:Simple_Lie_algebra dbr:Split_Lie_algebra dbr:Tits-Satake_diagram dbr:Tits_index dbr:Tits–Satake_diagram |
| is foaf:primaryTopic of |
wikipedia-en:Satake_diagram |