Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493136 | Journal of Algebra | 2005 | 18 Pages |
Abstract
A k-linear triangulated category A is called locally finite provided âXâindAdimkHomA(X,Y)<â for any indecomposable object Y in A. 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 LËn: By using this, we prove that the Auslander-Reiten quiver of any locally finite triangulated category A is of the form ZÎâ/G, where Î is a Dynkin diagram and G is an automorphism group of ZÎâ. For most automorphism groups G, the triangulated categories with ZÎâ/G as their Auslander-Reiten quivers are constructed. In particular, a triangulated category with LËn as its Auslander-Reiten quiver is constructed.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jie Xiao, Bin Zhu,