Auslander-Reiten-Serre duality for n-exangulated categories
JOURNAL OF ALGEBRA AND ITS APPLICATIONS(2024)
摘要
Let (l, E, s) be an Ext-finite, Krull Schmidt and k-linear n-exangulated category with k a commutative artinian ring. In this note, we prove that l has Auslander-Reiten-Serre duality if and only if l has Auslander-Reiten n-exangles. Moreover, we also give an equivalent condition for the existence of Serre duality (which is a special type of Auslander-Reiten-Serre duality). Finally, assume further that l has Auslander-Reiten-Serre duality. We exploit a bijection triangle, which involves the restricted Auslander bijection and the Auslander-Reiten-Serre duality.
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关键词
n-Exangulated categories,Auslander-Reiten n-exangles,Auslander-Reiten-Serre duality,Serre duality,Auslander bijection
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