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 and AR theory.
The Grothendieck Groups of Discrete Cluster Categories of Dynkin Type $A_{\infty}$
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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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math.RT 1years
2025 1verdicts
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Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory
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 and AR theory.