"Gabriel's theorem"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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==statement== | ==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 | ||
2014년 4월 23일 (수) 18:45 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