Gabriel's theorem

statement

thm (Gabriel)

A connected quiver Q has finite type iff the underlying graph is a Dynkin diagram of (A,D,E) type. Moreoever there is a bijection between {indecomposable kQ-modules} and {positive roots} \[M \to \dim M\] where \(\dim\) is dimension vector

idea of proof

• define tilting functor
• get Coxeter element

related items

• Quiver representations
• Coxeter functor and transformation

expositions

• Carroll, Gabriel's Theorem

메타데이터

위키데이터

• ID : Q5515505

Spacy 패턴 목록

• [{'LOWER': 'gabriel'}, {'LOWER': "'s"}, {'LEMMA': 'theorem'}]