Extensions of finitely presented and finitely co-presented representations

Details Extensions of finitely presented and finitely co-presented representations Extensions of finitely presented and finitely co-presented representations

2012-01-23

arxiv.org/abs/1201.4833v1

Mathematics

Representation Theory

28 pages, 1 figure

Scientific paper

Let Q be a strongly locally finite quiver and denote by rep(Q) the category of locally finite dimensional representations of Q over some fixed field k. We define a category C(Q) which is a full, abelian, Hom-finite and Krull-Schmidt subcategory of rep(Q) containing all the almost split sequences of rep(Q). We give the Auslander-Reiten quiver of C(Q) by describing its connected components. Finally, we prove that these connected components are also connected components of the Auslander-Reiten quiver of rep(Q).

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