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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.23354 |
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Table of Contents:
- Reading constructed a Cambrian lattice $C_Γ$ for each oriented finite type Coxeter diagram $Γ$. We show that the derived category of representations of $C_Γ$ is fractionally Calabi-Yau for any $Γ$, confirming a conjecture of Chapoton. This extends a result of Rognerud for Cambrian lattices of type $A$ with linear orientation, better known as Tamari lattices. If $Γ$ is crystallographic, then $C_Γ$ is given by the lattice of torsion classes of any hereditary algebra $Λ$ of type $Γ$. In this case we introduce and study a class of intervals in $C_Γ$ whose combinatorics matches the combinatorics of $2$-cluster tilting objects in the 2-cluster category of $Λ$. This allows us to compute the Calabi-Yau dimension of $C_Γ$.