The Quiver of Projectives in Hereditary Categories with Serre Duality

Details The Quiver of Projectives in Hereditary Categories with Serre Duality The Quiver of Projectives in Hereditary Categories with Serre Duality

2008-01-09

arxiv.org/abs/0801.1461v2

Mathematics

Representation Theory

16 pages, as accepted by Journal of Pure and Applied Algebra

Scientific paper

Let k be an algebraically closed field and A a k-linear hereditary category satisfying Serre duality with no infinite radicals between the preprojective objects. If A is generated by the preprojective objects, then we show that A is derived equivalent to rep_k Q for a so called strongly locally finite quiver Q. To this end, we introduce light cone distances and round trip distances on quivers which will be used to investigate sections in stable translation quivers of the form \mathbb{Z} Q.

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