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Syzygy Transformations of Cluster Characters and Geometric Twists
Abstract
We use the full multiplication formula to study syzygy and suspension of cluster characters. In stably 2-Calabi--Yau Frobenius categories, syzygy and cosyzygy induce inverse automorphisms of localized character algebras; in Hom-finite 2-Calabi--Yau triangulated categories, the same uniqueness principle transports all cluster characters under suspension. The latter gives our Auslander--Reiten F-polynomial identity. No mutation reachability is required. We extend positroid twist identities to all objects, recover the Grassmannian and unipotent-cell formulas, identify partition-function algebras before boundary localization, and derive tropical covariance when the relevant tropical coordinate map is a homeomorphism.
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BibTeX
@misc{fei2026syzygy,
title = {{Syzygy Transformations of Cluster Characters and Geometric Twists}},
author = {Jiarui Fei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10090},
eprint = {2609.10090},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10090},
}
RIS
TY - UNPB
TI - Syzygy Transformations of Cluster Characters and Geometric Twists
AU - Jiarui Fei
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10090
UR - https://arxiv.org/abs/2609.10090
AB - We use the full multiplication formula to study syzygy and suspension of cluster characters. In stably 2-Calabi--Yau Frobenius categories, syzygy and cosyzygy induce inverse automorphisms of localized character algebras; in Hom-finite 2-Calabi--Yau triangulated categories, the same uniqueness principle transports all cluster characters under suspension. The latter gives our Auslander--Reiten F-polynomial identity. No mutation reachability is required. We extend positroid twist identities to all objects, recover the Grassmannian and unipotent-cell formulas, identify partition-function algebras before boundary localization, and derive tropical covariance when the relevant tropical coordinate map is a homeomorphism.
ER -