Locally finite triangulated categories |
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Authors: | Jie Xiao Bin Zhu |
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Affiliation: | Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, PR China |
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Abstract: | A k-linear triangulated category is called locally finite provided for any indecomposable object Y in . It has Auslander–Reiten triangles. In this paper, we show that if a (connected) triangulated category has Auslander–Reiten triangles and contains loops, then its Auslander–Reiten quiver is of the form : By using this, we prove that the Auslander–Reiten quiver of any locally finite triangulated category is of the form , where Δ is a Dynkin diagram and G is an automorphism group of . For most automorphism groups G, the triangulated categories with as their Auslander–Reiten quivers are constructed. In particular, a triangulated category with as its Auslander–Reiten quiver is constructed. |
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Keywords: | Locally finite triangulated category Triangulated category with loops Auslander– Reiten quiver Dynkin diagram |
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