The Grothendieck Groups of Discrete Cluster Categories of Dynkin Type $A_{\infty}$

Dave Murphy

The Grothendieck Groups of Discrete Cluster Categories of Dynkin Type $A_{\infty}$

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arxiv 2206.03911 v2 pith:AJW4R5NY submitted 2022-06-08 math.RT math.CT

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keywords categoriesclusterdiscretegrothendieckcomputedynkingroupsinfty

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abstract

In this work we compute the triangulated Grothendieck groups for each of the family of discrete cluster categories of Dynkin type $A_{\infty}$ as introduced by Holm-Jorgensen. Subsequently, we also compute the Grothendieck group of a completion of these discrete cluster categories in the sense of Paquette-Yildirim.

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Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory
math.RT 2025-08 unverdicted novelty 7.0 of 10

The paper constructs infinite discrete Nakayama representations via persistence theory and stabilizes them into negative Calabi-Yau versions of Igusa-Todorov discrete cluster categories of type A, with geometric model...

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