Noetherian 判据 for dimer 代数

On the central geometry of nonnoetherian dimer algebras

Let $Z$ be the center of a nonnoetherian dimer algebra on a torus. Although $Z$ itself is also nonnoetherian, we show that it has Krull dimension $3$, and is locally noetherian on an open dense set of $\operatorname{Max}Z$. Furthermore, we show that the reduced center $Z/\operatorname{nil}Z$ is depicted by a Gorenstein singularity, and contains precisely one closed point of positive geometric dimension.

非局部性与 dimer 代数的中心几何

Nonlocality and the central geometry of dimer algebras

本文证明不可消去 dimer 代数及其中心非 Noether、中心模无限生成，并刻画其约化中心的 Gorenstein 几何。

二聚体代数、ghor 代数和循环收缩

Dimer algebras, ghor algebras, and cyclic contractions

本文研究环面上 ghor 代数与二聚体代数的关系，证明诺特性等价于二聚体代数，并分类最大维数简单模及描述中心，引入 Higgsing 和介子手性环形式化概念。

Morita equivalences and Azumaya loci from Higgsing dimer algebras

Let $ψ: A \to A'$ be a cyclic contraction of dimer algebras, with $A$ non-cancellative and $A'$ cancellative. $A'$ is then prime, noetherian, and a finitely generated module over its center. In contrast, $A$ is often not prime, nonnoetherian, and an infinitely generated module over its center. We present certain Morita equivalences that relate the representation theory of $A$ with that of $A'$. We then characterize the Azumaya locus of $A$ in terms of the Azumaya locus of $A'$, and give an explicit classification of the simple $A$-modules parameterized by the Azumaya locus. Furthermore, we sho…

局部测地线ghor代数的整体维数

Global dimensions of local geodesic ghor algebras

本文研究紧曲面ghor代数的局部化整体维数，证明其循环局部化整体维数上界为2g+1且与中心Krull维数一致，还给出上界取等的充要条件。