The generalized Auslander–Reiten duality on an exact category
The generalized Auslander–Reiten duality on an exact category
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DOI：
10.1142/s0219498818502274
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发表时间：
2016-09
影响因子：
0.8
通讯作者：
Pengjie Jiao
中科院分区：
文献类型：
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作者：
Pengjie Jiao
我们在Hom-有限Krull-Schmidt正合范畴上引入了广义Auslander-Reiten对偶的概念[公式：见正文]。这种对偶性导致了广义的Auslander-Reiten平移函子[公式：见文本]和[公式：见文本]。它们是[公式：见文本]的两个满子范畴[公式：见文本]和[公式：见文本]的稳定范畴之间的相互准逆等价。非射影不可分解对象位于[公式：See Text]的定义域中当且仅当它作为几乎分裂合并的第三项出现；对偶，非内射不可分解对象位于[公式：See Text]的定义域中当且仅当它作为几乎分裂合并的第一项出现。我们研究局部有限区间有限箭图的有限表示范畴上的广义Auslander-Reiten对偶。
We introduce a notion of generalized Auslander–Reiten duality on a Hom-finite Krull–Schmidt exact category [Formula: see text]. This duality induces the generalized Auslander–Reiten translation functors [Formula: see text] and [Formula: see text]. They are mutually quasi-inverse equivalences between the stable categories of two full subcategories [Formula: see text] and [Formula: see text] of [Formula: see text]. A non-projective indecomposable object lies in the domain of [Formula: see text] if and only if it appears as the third term of an almost split conflation; dually, a non-injective indecomposable object lies in the domain of [Formula: see text] if and only if it appears as the first term of an almost split conflation. We study the generalized Auslander–Reiten duality on the category of finitely presented representations of locally finite interval-finite quivers.