PreprintarXiv licencearXiv
Phantom categories on 3-vertex directed DG quivers
Abstract
We construct infinitely many pairwise non-derived-Morita-equivalent phantom categories 𝒫m, m∈ℤ from concrete directed DG quivers with 3 vertices. Moreover, there exists a fixed finite-dimensional DG algebra C such that for each m∈ℤ, there is a way to reassign cohomological gradings on C (without changing the differential) to obtain a new DG algebra Cm with Perf(Cm)≅ 𝒫m.
Related
BibTeX
@misc{liu2026phantom,
title = {{Phantom categories on 3-vertex directed DG quivers}},
author = {Yeqin Liu and Yu Shen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27191},
eprint = {2609.27191},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27191},
}
RIS
TY - UNPB
TI - Phantom categories on 3-vertex directed DG quivers
AU - Yeqin Liu
AU - Yu Shen
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27191
UR - https://arxiv.org/abs/2609.27191
AB - We construct infinitely many pairwise non-derived-Morita-equivalent phantom categories 𝒫_m, m∈ℤ from concrete directed DG quivers with 3 vertices. Moreover, there exists a fixed finite-dimensional DG algebra C such that for each m∈ℤ, there is a way to reassign cohomological gradings on C (without changing the differential) to obtain a new DG algebra C_m with Perf(C_m)≅ 𝒫_m.
ER -