"Gabriel's theorem"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| 4번째 줄: | 4번째 줄: | ||
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} | 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 |
2020년 11월 16일 (월) 04:36 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