"Gabriel's theorem"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) (→메타데이터: 새 문단) |
Pythagoras0 (토론 | 기여) |
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| 3번째 줄: | 3번째 줄: | ||
;thm (Gabriel) | ;thm (Gabriel) | ||
| − | A connected quiver Q has finite type iff the underlying graph is a Dynkin | + | 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} |
:<math>M \to \dim M</math> | :<math>M \to \dim M</math> | ||
where <math>\dim</math> is dimension vector | where <math>\dim</math> is dimension vector | ||
| − | + | ||
| − | + | ||
==idea of proof== | ==idea of proof== | ||
| 16번째 줄: | 16번째 줄: | ||
* get Coxeter element | * get Coxeter element | ||
| − | + | ||
2020년 12월 28일 (월) 05:26 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
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위키데이터
- ID : Q5515505