Weight (representation theory) (original) (raw)

About DBpedia

In der Darstellungstheorie der Lie-Algebren, einem Teilgebiet der Mathematik, sind Gewichte gewisse lineare Abbildungen. Sie sind unter anderem deshalb von Bedeutung, weil Darstellungen von Lie-Gruppen und Lie-Algebren durch ihr höchstes Gewicht klassifiziert werden.

thumbnail

Property Value
dbo:abstract In der Darstellungstheorie der Lie-Algebren, einem Teilgebiet der Mathematik, sind Gewichte gewisse lineare Abbildungen. Sie sind unter anderem deshalb von Bedeutung, weil Darstellungen von Lie-Gruppen und Lie-Algebren durch ihr höchstes Gewicht klassifiziert werden. (de) In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space. (en) 리 대수 이론에서, 무게(영어: weight)는 리 대수의 표현을 분류하는 일련의 수들이다. (ko) 表現論という数学の分野において,体 F 上の代数 A のウェイト(英: weight)とは,A から F へのである,あるいは同じことだが,A の F 上の1次元表現である.それは群のの代数の類似である.しかしながら,概念の重要性は,リー環の表現への,したがって代数群やリー群の表現への,その応用から生じる.この文脈では,表現のウェイトは固有値の概念の一般化であり,対応する固有空間はウェイト空間と呼ばれる. (ja) У теорії представлень вагою алгебри A над полем F називається гомоморфізм із A у поле F, або еквівалентно одновимірне представлення A над полем F. Воно є певною мірою аналогом мультиплікативного характеру групи. Подібне поняття також є для алгебр Лі, у цьому випадку вага представлення є узагальненням власного значення, і відповідний власний простір називається ваговим простором. (uk)
dbo:thumbnail wiki-commons:Special:FilePath/Weights_for_A2_root_system.png?width=300
dbo:wikiPageExternalLink https://archive.org/details/introductiontoli00jame
dbo:wikiPageID 277179 (xsd:integer)
dbo:wikiPageLength 19715 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID 1117039431 (xsd:integer)
dbo:wikiPageWikiLink dbr:Multiplicative_group dbr:Representation_theory dbr:Coroot dbr:Algebra_homomorphism dbr:Algebra_over_a_field dbr:Algebra_representation dbr:Algebraic_group dbr:Vector_space dbr:Lie_algebra_representation dbr:Lie_group dbc:Lie_algebras dbc:Representation_theory_of_Lie_groups dbr:Commutator dbr:Mathematics dbr:Matrix_(mathematics) dbr:Quotient_module dbr:Eigenbasis dbr:Eigenspace dbr:Eigenvalue dbr:Eigenvector dbr:Lie_algebra dbr:Commuting_matrices dbr:Compact_group dbr:Fundamental_group dbr:Identity_element dbr:Lattice_(group) dbr:Linear_map dbr:Field_(mathematics) dbr:Linear_functional dbr:Representation_(mathematics) dbr:Group_(mathematics) dbr:Adjoint_representation_of_a_Lie_algebra dbr:Irreducible_(representation_theory) dbr:Abelian_Lie_algebra dbc:Representation_theory_of_Lie_algebras dbr:Highest-weight_category dbr:Diagonalizable_matrix dbr:Group_representation dbr:Group_theory dbr:Multiplicative_character dbr:Root_system dbr:Verma_module dbr:Linear_transformation dbr:Semisimple_operator dbr:Simply_connected dbr:Simultaneously_diagonalize dbr:Springer-Verlag dbr:Quotient_(group_theory) dbr:Derived_algebra dbr:Positive_root dbr:File:Weights_for_A2_root_system.png dbr:File:A2example.pdf dbr:File:Illustration_of_notion_of_"higher"_for_root_systems.png
dbp:wikiPageUsesTemplate dbt:Anchor dbt:Citation dbt:Main dbt:Ref_begin dbt:Refend dbt:Reflist dbt:See_also dbt:Visible_anchor dbt:Fulton-Harris
dct:subject dbc:Lie_algebras dbc:Representation_theory_of_Lie_groups dbc:Representation_theory_of_Lie_algebras
gold:hypernym dbr:Homomorphism
rdf:type owl:Thing yago:WikicatLieAlgebras yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:Science105999797
rdfs:comment In der Darstellungstheorie der Lie-Algebren, einem Teilgebiet der Mathematik, sind Gewichte gewisse lineare Abbildungen. Sie sind unter anderem deshalb von Bedeutung, weil Darstellungen von Lie-Gruppen und Lie-Algebren durch ihr höchstes Gewicht klassifiziert werden. (de) In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space. (en) 리 대수 이론에서, 무게(영어: weight)는 리 대수의 표현을 분류하는 일련의 수들이다. (ko) 表現論という数学の分野において,体 F 上の代数 A のウェイト(英: weight)とは,A から F へのである,あるいは同じことだが,A の F 上の1次元表現である.それは群のの代数の類似である.しかしながら,概念の重要性は,リー環の表現への,したがって代数群やリー群の表現への,その応用から生じる.この文脈では,表現のウェイトは固有値の概念の一般化であり,対応する固有空間はウェイト空間と呼ばれる. (ja) У теорії представлень вагою алгебри A над полем F називається гомоморфізм із A у поле F, або еквівалентно одновимірне представлення A над полем F. Воно є певною мірою аналогом мультиплікативного характеру групи. Подібне поняття також є для алгебр Лі, у цьому випадку вага представлення є узагальненням власного значення, і відповідний власний простір називається ваговим простором. (uk)
rdfs:label Gewicht (Darstellung) (de) 무게 (표현론) (ko) ウェイト (表現論) (ja) Weight (representation theory) (en) Вага (теорія представлень) (uk)
rdfs:seeAlso dbr:Representation_theory_of_semisimple_Lie_algebras
owl:sameAs freebase:Weight (representation theory) yago-res:Weight (representation theory) wikidata:Weight (representation theory) dbpedia-de:Weight (representation theory) dbpedia-ja:Weight (representation theory) dbpedia-ko:Weight (representation theory) dbpedia-uk:Weight (representation theory) https://global.dbpedia.org/id/4xQFy
prov:wasDerivedFrom wikipedia-en:Weight_(representation_theory)?oldid=1117039431&ns=0
foaf:depiction wiki-commons:Special:FilePath/Illustration_of_notion_of_"higher"_for_root_systems.png wiki-commons:Special:FilePath/Weights_for_A2_root_system.png
foaf:isPrimaryTopicOf wikipedia-en:Weight_(representation_theory)
is dbo:wikiPageDisambiguates of dbr:Weight_(disambiguation)
is dbo:wikiPageRedirects of dbr:Dominant_weight dbr:Fundamental_weight dbr:Weight_space_(representation_theory) dbr:Weight_module dbr:Simple_highest_weight_module dbr:Simultaneous_eigenvector dbr:Fundamental_Weyl_chamber dbr:Coweight dbr:Lowest_weight dbr:Lowest_weight_representation dbr:Highest-weight_module dbr:Highest-weight_representation dbr:Highest_weight dbr:Highest_weight_module dbr:Highest_weight_modules dbr:Highest_weight_representation dbr:Highest_weight_vector dbr:Integral_weight dbr:Weight_(Lie_algebra) dbr:Weight_(Lie_algebras) dbr:Weight_diagram dbr:Weight_lattice dbr:Weight_modules dbr:Weight_spaces dbr:Weight_subspace dbr:Weight_vector
is dbo:wikiPageWikiLink of dbr:Representation_theory dbr:Borel–Weil–Bott_theorem dbr:Algebra_representation dbr:Algebraic_torus dbr:Representation_theory_of_the_Lorentz_group dbr:Cubic_surface dbr:Lie_algebra_representation dbr:List_of_representation_theory_topics dbr:'t_Hooft_loop dbr:An_Exceptionally_Simple_Theory_of_Everything dbr:Generalized_Verma_module dbr:Eigenvalues_and_eigenvectors dbr:Conformal_family dbr:Compact_group dbr:Demazure_module dbr:Fundamental_representation dbr:Dominant_weight dbr:Fundamental_weight dbr:Pi_(letter) dbr:Zonal_spherical_function dbr:Gan–Gross–Prasad_conjecture dbr:K-stability dbr:Adjoint_representation dbr:Isotypic_component dbr:Kostant_partition_function dbr:List_of_Lie_groups_topics dbr:Character_theory dbr:Charge_(physics) dbr:Ladder_operator dbr:Holstein–Primakoff_transformation dbr:Weight_(disambiguation) dbr:Weight_space_(representation_theory) dbr:Wilson_loop dbr:Spin_representation dbr:Spinor dbr:Category_O dbr:Ranee_Brylinski dbr:Root_system dbr:Verma_module dbr:Virasoro_algebra dbr:Ethical_positioning_index dbr:Wess–Zumino–Witten_model dbr:Weyl_character_formula dbr:Representation_theory_of_semisimple_Lie_algebras dbr:Theorem_of_the_highest_weight dbr:Weyl_group dbr:Weight_module dbr:Simple_highest_weight_module dbr:Simultaneous_eigenvector dbr:Fundamental_Weyl_chamber dbr:Coweight dbr:Lowest_weight dbr:Lowest_weight_representation dbr:Highest-weight_module dbr:Highest-weight_representation dbr:Highest_weight dbr:Highest_weight_module dbr:Highest_weight_modules dbr:Highest_weight_representation dbr:Highest_weight_vector dbr:Integral_weight dbr:Weight_(Lie_algebra) dbr:Weight_(Lie_algebras) dbr:Weight_diagram dbr:Weight_lattice dbr:Weight_modules dbr:Weight_spaces dbr:Weight_subspace dbr:Weight_vector
is rdfs:seeAlso of dbr:Root_system dbr:Representation_theory_of_semisimple_Lie_algebras dbr:Theorem_of_the_highest_weight
is foaf:primaryTopic of wikipedia-en:Weight_(representation_theory)