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arXiv · 2609.27191

Phantom categories on 3-vertex directed DG quivers

Yeqin Liu·Yu Shen
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Abstract

We construct infinitely many pairwise non-derived-Morita-equivalent phantom categories $\mathcal{P}_{m}, m\in\mathbb{Z}$ from concrete directed DG quivers with 3 vertices. Moreover, there exists a fixed finite-dimensional DG algebra $C$ such that for each $m\in\mathbb{Z}$, there is a way to reassign cohomological gradings on $C$ (without changing the differential) to obtain a new DG algebra $C_{m}$ with $\mathrm{Perf}(C_{m})\cong \mathcal{P}_{m}$.

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Yeqin Liu, Yu Shen. 2026-09-23. Phantom categories on 3-vertex directed DG quivers. https://arxiv.org/abs/2609.27191

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