Gabriel's theorem
imported>Pythagoras0님의 2020년 11월 14일 (토) 00:59 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 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
Kac theorem
expositions
- Carroll, Gabriel's Theorem