结理论和聚类代数 III：Posets

arXiv - MATH - Representation Theory Pub Date : 2024-09-17 DOI:arxiv-2409.11287

Véronique Bazier-Matte, Ralf Schiffler

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引用次数: 0

摘要

在以前的工作中，我们将一个模块 $T(i)$ 与链接图 $K$ 的每个段 $i$ 关联起来，并证明了 $T(i)$ 的子模块与 $K$ 相对于 $i$ 的考夫曼态之间存在着正集同构。在本文中，我们证明了这两个正集都是分布网格，并给出了这两个正集中的连接非还原性的明确描述。我们还证明了连接不可还原考夫曼态的子集合与 $T(i)$ 的系数 quiver 的集合同构。

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Knot theory and cluster algebra III: Posets

In previous work, we associated a module $T(i)$ to every segment $i$ of a link diagram $K$ and showed that there is a poset isomorphism between the submodules of $T(i)$ and the Kauffman states of $K$ relative to $i$. 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 $T(i)$.

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arXiv - MATH - Representation Theory

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