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
  {indecomposable kQ-modules} -> {positive roots}
  M -> dim M (dimension vector)
  

 

 

idea of proof

• define tilting functor
• get Coxeter element