"Gabriel's theorem"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 5개는 보이지 않습니다) | |||
| 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> | |
| − | where | + | where <math>\dim</math> is dimension vector |
| − | + | ||
| − | + | ||
==idea of proof== | ==idea of proof== | ||
| 16번째 줄: | 16번째 줄: | ||
* get Coxeter element | * get Coxeter element | ||
| − | + | ||
| 25번째 줄: | 25번째 줄: | ||
==related items== | ==related items== | ||
* [[Quiver representations]] | * [[Quiver representations]] | ||
| − | + | * [[Coxeter functor and transformation]] | |
==expositions== | ==expositions== | ||
| 34번째 줄: | 34번째 줄: | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
[[분류:math]] | [[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'}]