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PreprintCC BY 4.0arXiv

A refined multiplication formula in 2-Calabi-Yau Frobenius extriangulated categories

  • Ming Ding
  • Fan Xu
  • Panyue Zhou
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Abstract

We prove a multiplication formula for the Wang-Wei-Zhang cluster character on a Hom-finite $2$-Calabi--Yau Frobenius extriangulated category π’ž with a cluster-tilting object under the assumption that its stable category has constructible cones with respect to the induced cluster-tilting object. This formula generalizes those obtained by Wang-Wei-Zhang for π’ž in the one-dimensional case and by Keller-Plamondon-Qin for (stably) $2$-Calabi-Yau Frobenius or triangulated categories. As a consequence, we express the frozen term in an Auslander-Reiten mesh with the character of a minimal cosyzygy middle term. For acyclic quivers with principal coefficients, we compute these frozen multiplicities in Higgs categories and obtain explicit principal coefficient mesh relations.

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Cite

BibTeXRIS
BibTeX
@misc{ding2026refined,
  title = {{A refined multiplication formula in 2-Calabi-Yau Frobenius extriangulated categories}},
  author = {Ming Ding and Fan Xu and Panyue Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20049},
  eprint = {2609.20049},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20049},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A refined multiplication formula in 2-Calabi-Yau Frobenius extriangulated categories
AU  - Ming Ding
AU  - Fan Xu
AU  - Panyue Zhou
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20049
UR  - https://arxiv.org/abs/2609.20049
AB  - We prove a multiplication formula for the Wang-Wei-Zhang cluster character on a Hom-finite $2$-Calabi--Yau Frobenius extriangulated category π’ž with a cluster-tilting object under the assumption that its stable category has constructible cones with respect to the induced cluster-tilting object. This formula generalizes those obtained by Wang-Wei-Zhang for π’ž in the one-dimensional case and by Keller-Plamondon-Qin for (stably) $2$-Calabi-Yau Frobenius or triangulated categories. As a consequence, we express the frozen term in an Auslander-Reiten mesh with the character of a minimal cosyzygy middle term. For acyclic quivers with principal coefficients, we compute these frozen multiplicities in Higgs categories and obtain explicit principal coefficient mesh relations.
ER  -