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arXiv · 2510.06088

$(P,ϕ)$-Tamari lattices

Adrien Segovia
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Abstract

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.

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Adrien Segovia. 2025-10-07. $(P,ϕ)$-Tamari lattices. https://arxiv.org/abs/2510.06088

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