| dbo:abstract |
Der Darstellungsring einer Gruppe ist in der Mathematik vor allem in der Darstellungstheorie, aber auch in Algebra, Topologie und K-Theorie von Bedeutung. (de) In mathematics, especially in the area of algebra known as representation theory, the representation ring (or Green ring after J. A. Green) of a group is a ring formed from all the (isomorphism classes of the) finite-dimensional linear representations of the group. Elements of the representation ring are sometimes called virtual representations. For a given group, the ring will depend on the base field of the representations. The case of complex coefficients is the most developed, but the case of algebraically closed fields of characteristic p where the Sylow p-subgroups are cyclic is also theoretically approachable. (en) 리 군론에서 표현환(表現環, 영어: representation ring)은 어떤 리 군의 유한 차원 표현들로 생성되는 그로텐디크 환이다. (ko) |
| dbo:wikiPageExternalLink |
http://www.numdam.org/item/PMIHES_1968__34__113_0/ https://archive.org/details/explicitbrauerin0000snai |
| dbo:wikiPageID |
16673816 (xsd:integer) |
| dbo:wikiPageLength |
6981 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1090745620 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Cambridge_University_Press dbr:Sandy_Green_(mathematician) dbr:Representation_theory dbr:Algebraically_closed_field dbr:Character_group dbc:Group_theory dbc:Ring_theory dbr:Mathematics dbr:Λ-ring dbc:Finite_groups dbc:Lie_groups dbr:Cyclic_group dbr:Exterior_power dbr:Graduate_Texts_in_Mathematics dbr:Ring_(mathematics) dbr:Group_(mathematics) dbc:Representation_theory_of_groups dbr:Abelian_group dbr:Abstract_algebra dbr:Character_theory dbr:Sylow_subgroup dbr:Tensor_product_of_representations dbr:Modular_representation_theory dbr:Class_function dbr:Group_representation dbr:Group_ring dbr:Symmetric_group dbr:Springer-Verlag dbr:Characteristic_of_a_ring dbr:Grothendieck_ring dbr:Adams_operations |
| dbp:wikiPageUsesTemplate |
dbt:Citation dbt:Reflist |
| dct:subject |
dbc:Group_theory dbc:Ring_theory dbc:Finite_groups dbc:Lie_groups dbc:Representation_theory_of_groups |
| gold:hypernym |
dbr:Ring |
| rdf:type |
dbo:AnatomicalStructure yago:WikicatLieGroups yago:Abstraction100002137 yago:Group100031264 yago:WikicatFiniteGroups |
| rdfs:comment |
Der Darstellungsring einer Gruppe ist in der Mathematik vor allem in der Darstellungstheorie, aber auch in Algebra, Topologie und K-Theorie von Bedeutung. (de) In mathematics, especially in the area of algebra known as representation theory, the representation ring (or Green ring after J. A. Green) of a group is a ring formed from all the (isomorphism classes of the) finite-dimensional linear representations of the group. Elements of the representation ring are sometimes called virtual representations. For a given group, the ring will depend on the base field of the representations. The case of complex coefficients is the most developed, but the case of algebraically closed fields of characteristic p where the Sylow p-subgroups are cyclic is also theoretically approachable. (en) 리 군론에서 표현환(表現環, 영어: representation ring)은 어떤 리 군의 유한 차원 표현들로 생성되는 그로텐디크 환이다. (ko) |
| rdfs:label |
Darstellungsring (de) 표현환 (ko) Representation ring (en) |
| owl:sameAs |
freebase:Representation ring yago-res:Representation ring wikidata:Representation ring dbpedia-de:Representation ring dbpedia-ko:Representation ring https://global.dbpedia.org/id/4tzbb |
| prov:wasDerivedFrom |
wikipedia-en:Representation_ring?oldid=1090745620&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Representation_ring |
| is dbo:wikiPageRedirects of |
dbr:Character_ring |
| is dbo:wikiPageWikiLink of |
dbr:Depth_of_noncommutative_subrings dbr:Bott_cannibalistic_class dbr:Principal_indecomposable_module dbr:Λ-ring dbr:Kostant_polynomial dbr:Ring_(mathematics) dbr:Atiyah–Segal_completion_theorem dbr:Burnside_ring dbr:Michael_Atiyah dbr:Category_of_representations dbr:Segal's_conjecture dbr:Character_ring |
| is foaf:primaryTopic of |
wikipedia-en:Representation_ring |