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arXiv · 2609.20049

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 $\mathcal C$ 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 $\mathcal C$ 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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Ming Ding, Fan Xu, Panyue Zhou. 2026-09-17. A refined multiplication formula in 2-Calabi-Yau Frobenius extriangulated categories. https://arxiv.org/abs/2609.20049

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