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Simple-minded systems and reduction for negative Calabi-Yau triangulated categories

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arxiv 1808.02519 v1 pith:NKCFXWHO submitted 2018-08-07 math.RT

Raquel Coelho Simoes , David Pauksztello This is my paper · ORCID
classification math.RT
keywords simple-mindedsystemscalabi-yaucategoriestriangulatednegativereductiontechnique
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abstract

We develop the basic properties of $w$-simple-minded systems in $(-w)$-Calabi-Yau triangulated categories for $w \geq 1$. The main result is a reduction technique for negative Calabi-Yau triangulated categories. We show that the theory of simple-minded systems exhibits striking parallels with that of cluster-tilting objects. Our construction provides an inductive technique for constructing simple-minded systems.

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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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