Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:quivers
finite-dimensional algebras |
| gptkbp:characterizedBy |
quivers of finite representation type
|
| gptkbp:describes |
classification of finite-dimensional algebras of finite representation type
|
| gptkbp:field |
gptkb:algebra
representation theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Gabriel's theorem
|
| gptkbp:implies |
classification of indecomposable representations by positive roots of Dynkin diagrams
|
| gptkbp:namedAfter |
gptkb:Peter_Gabriel
gptkb:Pierre_Gabriel |
| gptkbp:publishedIn |
gptkb:Bulletin_de_la_Société_Mathématique_de_France
|
| gptkbp:relatedTo |
gptkb:Dynkin_diagrams
algebraically closed fields representation type quiver representations |
| gptkbp:state |
A finite-dimensional algebra over an algebraically closed field has only finitely many indecomposable representations up to isomorphism if and only if its underlying quiver is a disjoint union of Dynkin diagrams of type A, D, or E.
|
| gptkbp:yearProved |
1972
|
| gptkbp:bfsParent |
gptkb:Pierre_Gabriel
|
| gptkbp:bfsLayer |
5
|