Auslander-Gorenstein algebras and precluster tilting
Auslander-Gorenstein algebras and precluster tilting
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DOI：
10.1016/j.aim.2017.11.025
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
O. Iyama;Oyvind Solberg
中科院分区：
文献类型：
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作者：
O. Iyama;Oyvind Solberg
本文将n-簇倾斜子范畴和τ-自内射代数的概念推广到n-预簇倾斜子范畴和τ n-自内射代数，证明了与n-预簇倾斜子范畴自然相关的子范畴具有更高的Auslander-Reiten理论.此外，我们给出了n-预聚群倾斜子范畴与n-极小Auslander-Gorenstein代数之间的一个双射，它是Auslander-Solberg对应[8]的高维模拟，也是n-Auslander对应[22]的Gorenstein模拟。利用与n-预簇倾斜子范畴相关联的Auslander-Reiten理论，将n-极小Auslander-Gorenstein代数分成4个不相交类.我们的方法是基于相对同调代数由于Auslander-Solberg。
We generalize the notions of n-cluster tilting subcategories and τ-selfinjective algebras into n-precluster tilting subcategories and τ n-selfinjective algebras, where we show that a subcategory naturally associated to n-precluster tilting subcategories has a higher Auslander–Reiten theory. Furthermore, we give a bijection between n-precluster tilting subcategories and n-minimal Auslander–Gorenstein algebras, which is a higher dimensional analog of Auslander–Solberg correspondence [8] as well as a Gorenstein analog of n-Auslander correspondence [22]. The Auslander–Reiten theory associated to an n-precluster tilting subcategory is used to classify the n-minimal Auslander–Gorenstein algebras into four disjoint classes. Our method is based on relative homological algebra due to Auslander–Solberg.