Knot theory and cluster algebra III: Posets
Combinatorics
2024-09-18 v1 Geometric Topology
Representation Theory
Abstract
In previous work, we associated a module to every segment of a link diagram and showed that there is a poset isomorphism between the submodules of and the Kauffman states of relative to . In this paper, we show that the posets are distributive lattices and give explicit descriptions of the join irreducibles in both posets. We also prove that the subposet of join irreducible Kauffman states is isomorphic to the poset of the coefficient quiver of .
Cite
@article{arxiv.2409.11287,
title = {Knot theory and cluster algebra III: Posets},
author = {Véronique Bazier-Matte and Ralf Schiffler},
journal= {arXiv preprint arXiv:2409.11287},
year = {2024}
}