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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.06088 |
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Table of Contents:
- Given any poset $P$ and chain $ϕ$ in $P$, we define the $(P,ϕ)$-Tamari lattice. We study in depth these lattices and prove in particular that they are join-semidistributive, join-congruence uniform and left modular. We prove that the lattices of higher torsion classes of the higher Auslander and Nakayama algebras of type $\mathbb{A}$ are examples of $(P,ϕ)$-Tamari lattices and thus they inherit their properties. We also give general results related to left modular, extremal and congruence normal lattices.