Representation theory of strongly locally finite quivers
Representation theory of strongly locally finite quivers
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DOI：
10.1112/plms/pds039
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发表时间：
2013-01
影响因子：
1.8
通讯作者：
R. Bautista;Shiping Liu;Charles Paquette
中科院分区：
文献类型：
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作者：
R. Bautista;Shiping Liu;Charles Paquette
本文研究强、局部有限振动的表示理论。我们首先研究了有限呈现和共呈现表象的一些性质，然后在局部有限维表象的范畴内构造了一些以有限共呈现表象开始，以有限呈现表象结束的几乎分裂序列。进一步，我们得到了有限表示范畴的Auslander-Reiten分量形状的一般描述，并证明正则Auslander-Reiten分量的数目是无限的当且仅当颤振不是有限或无限Dynkin型时。在无限Dynkin情况下，我们将给出不可分解表示的完整列表和对Auslander-Reiten分量的明确描述。最后，我们应用这些结果在有限表示的有界复合体的派生范畴中研究了Auslander-Reiten理论。
This paper deals with the representation theory of strongly, locally finite quivers. We first study some properties of the finitely presented or co‐presented representations, and then construct in the category of locally finite‐dimensional representations some almost split sequences which start with a finitely co‐presented representation and end with a finitely presented representation. Furthermore, we obtain a general description of the shapes of the Auslander–Reiten components of the category of finitely presented representations and prove that the number of regular Auslander–Reiten components is infinite if and only if the quiver is not of finite or infinite Dynkin type. In the infinite Dynkin case, we shall give a complete list of the indecomposable representations and an explicit description of the Auslander–Reiten components. Finally, we apply these results to study the Auslander–Reiten theory in the derived category of bounded complexes of finitely presented representations.