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The derived category of a quiver

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A quiver is a bunch of arrows. Their representations provide an important subclass of representations of algebras. Gabriel’s Theorem classifies when the representation theory of a quiver is finite. In the proof of this theorem, it appears that there is some common information shared by quivers with the same underlying graph. This common information is encoded in the derived category of a quiver which has a very nice description as the mesh quiver. I’ll work this all through with the example of A3. The talk is based on the results in the following paper.

Happel, Dieter. “On the derived category of a finite-dimensional algebra..” Commentarii mathematici Helvetici 62 (1987): 339-389.

This talk is part of the Junior Algebra and Number Theory seminar series.

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