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Gabriel's theorem

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Statement

Gabriel's theorem (Gabriel 72) says that connected quivers with a finite number of indecomposable quiver representations over an algebraically closed field are precisely the Dynkin quivers: those whose underlying undirected graph is a Dynkin diagram in the ADE series.

Moreover, the indecomposable quiver representations in this case are in bijection with the positive roots in the root system of the Dynkin diagram.

References

The result is due to

Lecture notes include

Last revised on January 22, 2019 at 06:52:13. See the history of this page for a list of all contributions to it.