Auslander correspondence for triangulated categories
Auslander correspondence for triangulated categories
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DOI：
10.2140/ant.2020.14.2037
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发表时间：
2018-05
期刊：
影响因子：
--
通讯作者：
Norihiro Hanihara
中科院分区：
文献类型：
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作者：
Norihiro Hanihara
我们给出满足某些有限性条件的两类三角范畴的 Auslander 对应的类似物。第一类是带有加性生成元的三角范畴，我们将它们的自同态代数视为 Auslander 代数。对于第二个，我们引入 $[1]$-加法生成器的概念，并将其分级自同态代数视为 Auslander 代数。我们给出了每个类的 Auslander 代数的同调特征。在此过程中，我们还证明了同伦范畴上的代数三角形结构在等价性方面是唯一的。
We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism algebras as the Auslander algebras. For the second one, we introduce the notion of $[1]$-additive generators and consider their graded endormorphism algebras as the Auslander algebras. We give a homological characterization of the Auslander algebras for each class. Along the way, we also show that the algebraic triangle structures on the homotopy categories are unique up to equivalence.