"Gabriel's theorem"의 두 판 사이의 차이

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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 diagram of (A,D,E) type. Moreoever there is a bijection between {indecomposable kQ-modules} and {positive roots}
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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
  
 
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==idea of proof==
 
==idea of proof==
16번째 줄: 16번째 줄:
 
* get Coxeter element
 
* get Coxeter element
  
 
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2020년 12월 28일 (월) 04:26 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

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expositions

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