"Gabriel's theorem"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
imported>Pythagoras0 |
imported>Pythagoras0 |
||
| 25번째 줄: | 25번째 줄: | ||
==related items== | ==related items== | ||
* [[Quiver representations]] | * [[Quiver representations]] | ||
| − | + | * [[Coxeter functor and transformation]] | |
==expositions== | ==expositions== | ||
2015년 8월 4일 (화) 05:06 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