"Gabriel's theorem"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| − | + | ==Kac theorem== | |
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==related items== | ==related items== | ||
* [[Quiver representations]] | * [[Quiver representations]] | ||
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| + | ==expositions== | ||
| + | * Carroll, [http://www.math.missouri.edu/~carrollat/files/Quiver_Lecture.pdf Gabriel's Theorem] | ||
[[분류:개인노트]] | [[분류:개인노트]] | ||
2014년 4월 14일 (월) 18:42 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
{indecomposable kQ-modules} -> {positive roots}
M -> dim M (dimension vector)
idea of proof
- define tilting functor
- get Coxeter element
Kac theorem
expositions
- Carroll, Gabriel's Theorem