"Gabriel's theorem"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 17개는 보이지 않습니다) | |||
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| − | + | ==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} | |
| + | :<math>M \to \dim M</math> | ||
| + | where <math>\dim</math> is dimension vector | ||
| − | + | ||
| − | + | ||
| + | |||
| + | ==idea of proof== | ||
* define tilting functor | * define tilting functor | ||
* get Coxeter element | * get Coxeter element | ||
| − | + | ||
| + | |||
| + | |||
| + | ==Kac theorem== | ||
| + | |||
| + | |||
| − | + | ==related items== | |
| + | * [[Quiver representations]] | ||
| + | * [[Coxeter functor and transformation]] | ||
| − | + | ==expositions== | |
| + | * Carroll, [http://www.math.missouri.edu/~carrollat/files/Quiver_Lecture.pdf Gabriel's Theorem] | ||
| − | + | [[분류:개인노트]] | |
| + | [[분류:cluster algebra]] | ||
| + | [[분류:math and physics]] | ||
| + | [[분류:math]] | ||
| + | [[분류:migrate]] | ||
| − | * | + | ==메타데이터== |
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q5515505 Q5515505] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'gabriel'}, {'LOWER': "'s"}, {'LEMMA': 'theorem'}] | ||
2021년 2월 17일 (수) 01:06 기준 최신판
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
메타데이터
위키데이터
- ID : Q5515505
Spacy 패턴 목록
- [{'LOWER': 'gabriel'}, {'LOWER': "'s"}, {'LEMMA': 'theorem'}]