Gabriel's theorem
imported>Pythagoras0님의 2013년 10월 8일 (화) 06:29 판
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