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- W2004673265 abstract "We introduce a notion of generalized Serre duality on a Hom-finite Krull–Schmidt triangulated category T . This duality induces the generalized Serre functor on T , which is a linear triangle equivalence between two thick triangulated subcategories of T . Moreover, the domain of the generalized Serre functor is the smallest additive subcategory of T containing all the indecomposable objects which appear as the third term of an Auslander–Reiten triangle in T ; dually, the range of the generalized Serre functor is the smallest additive subcategory of T containing all the indecomposable objects which appear as the first term of an Auslander–Reiten triangle in T . We compute explicitly the generalized Serre duality on the bounded derived categories of artin algebras and of certain noncommutative projective schemes in the sense of Artin and Zhang. We obtain a characterization of Gorenstein algebras: an artin algebra A is Gorenstein if and only if the bounded homotopy category of finitely generated projective A -modules has Serre duality in the sense of Bondal and Kapranov." @default.
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- W2004673265 date "2011-02-01" @default.
- W2004673265 modified "2023-09-29" @default.
- W2004673265 title "Generalized Serre duality" @default.
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- W2004673265 doi "https://doi.org/10.1016/j.jalgebra.2010.08.022" @default.
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