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- W4385963584 abstract "We classify thick subcategories in a Paquette-Yi ldi ri m completion $overline{mathcal{C}}$ of a discrete cluster category of Dynkin type $A_{infty}$. To do this we introduce the notion of homologically connected objects, and the hc (=homologically connected) decomposition of an object into homologically connected objects in a $mathrm{Hom}$-finite, Krull-Schmidt triangulated category. We show that any object in a $overline{mathcal{C}}$ has a hc decomposition, and that the hc decomposition determines the thick closure of an object. Moreover, we use this result to classify the classical generators of $overline{mathcal{C}}$ as homologically connected objects satisfying a maximality condition. Every homologically connected object has an invariant, known as the homological length, and we show that in $overline{mathcal{C}}$ this homological length is an upper bound for the generation time of a classical generator. This allows us to provide an upper bound for the Orlov spectrum of $overline{mathcal{C}}$, as well as giving the Rouquier dimension." @default.
- W4385963584 created "2023-08-18" @default.
- W4385963584 creator A5004541278 @default.
- W4385963584 date "2023-08-03" @default.
- W4385963584 modified "2023-09-23" @default.
- W4385963584 title "Bounding The Orlov Spectrum For A Completion Of Discrete Cluster Categories" @default.
- W4385963584 doi "https://doi.org/10.48550/arxiv.2308.01767" @default.
- W4385963584 hasPublicationYear "2023" @default.
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