Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory

TL;DR

This paper introduces infinite discrete Nakayama representations using persistence theory, leading to negative Calabi-Yau triangulated categories that extend discrete cluster categories of type A, with detailed geometric and AR theory descriptions.

Contribution

It presents a novel construction of negative Calabi-Yau categories via stabilization of discrete Nakayama representations using persistence theory.

Findings

Construction of infinite discrete Nakayama representations.

Development of negative Calabi-Yau triangulated categories.

Description of geometric models and Auslander-Reiten theory.

Abstract

We introduce infinite discrete versions of the symmetric Nakayama representations by using techniques of persistence theory. After stabilising, we obtain a family triangulated categories which can be regarded as negative Calabi-Yau versions of the Igusa-Todorov discrete cluster categories of type A. We describe their geometric model and AR theory.