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Cluster categories coming from cyclic posets

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arxiv 1303.6697 v2 pith:RX2IR7PH submitted 2013-03-26 math.RT

Kiyoshi Igusa , Gordana Todorov This is my paper · ORCID
classification math.RT
keywords cyclicposetcategoriescategoryclusterconstructionexamplesa-infinity
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Cyclic poset are generalizations of cyclically ordered sets. In this paper we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The continuous cluster categories of arXiv:1209.1879 are examples of this construction. If we twist the construction using an admissible automorphism of the cyclic poset, we generate other examples such as the m-cluster category of type A-infinity (m>2).

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  1. 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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