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• W3000407848 abstract "For a finite dimensional algebra Λ $Lambda$ of finite representation type and an additive generator M $M$ for mod Λ $operatorname{mod}Lambda$ , we investigate the properties of the Yoneda algebra Γ = ⨁ i ⩾ 0 Ext Λ i ( M , M ) $Gamma =bigoplus _{i geqslant 0}operatorname{Ext}_Lambda ^i(M,M)$ . We show that Γ $Gamma$ is graded coherent and Gorenstein of self-injective dimension at most 1, and the graded singularity category D sg Z ( Γ ) $mathrm{D_{sg}^mathbb {Z}}(Gamma )$ of Γ $Gamma$ is triangle equivalent to the derived category of the stable Auslander algebra of Λ $Lambda$ . These results remain valid for representation-infinite algebras. For this we introduce the Yoneda category Y $mathcal {Y}$ of Λ $Lambda$ as the additive closure of the shifts of the Λ $Lambda$ -modules in the derived category D b ( mod Λ ) $mathrm{D^b}(operatorname{mod}Lambda )$ . We show that Y $mathcal {Y}$ is coherent and Gorenstein of self-injective dimension at most 1, and the singularity category of Y $mathcal {Y}$ is triangle equivalent to the derived category D b ( mod ( mod ̲ Λ ) ) $mathrm{D^b}(operatorname{mod}(operatorname{underline{operatorname{mod}}}Lambda ))$ of the stable category mod ̲ Λ $operatorname{underline{operatorname{mod}}}Lambda$ . To give a triangle equivalence, we apply the theory of realization functors. We show that any algebraic triangulated category has an f-category over itself by formulating the filtered derived category of a DG category, which assures the existence of a realization functor." @default.
• W3000407848 created "2020-01-23" @default.
• W3000407848 creator A5014193514 @default.
• W3000407848 date "2022-05-11" @default.
• W3000407848 modified "2023-09-27" @default.
• W3000407848 title "Yoneda algebras and their singularity categories" @default.
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• W3000407848 doi "https://doi.org/10.1112/plms.12441" @default.
• W3000407848 hasPublicationYear "2022" @default.
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