Dyck路径、配置空间与多面体对于线性Nakayama代数
Dyck Paths, Configuration Spaces and Polytopes For Linear Nakayama algebras
AI总结：
本文通过Dyck路径构造了与线性Nakayama代数相关的有限维代数、仿射代数簇和多面体，并给出了自然的构造方法。
摘要：
我们提出了一种组合模型，用于描述与$\mathbb{C} A_n$商环相关的配置空间和多面体，即线性有向$A_n$标架的路径代数，也就是上三角矩阵代数。这些商代数被称为线性Nakayama代数。此类配置空间最近由第二作者及其合作者为更一般的代数引入。在这一特殊设定中，我们提供了简单的证明和显式的组合构造。从Dyck路径出发，我们定义了三个相关对象：有限维代数、仿射代数簇和多面体。此外，我们的构造是自然的：每个Dyck路径的偏序中的关系都给定了相应对象之间的映射。
英文摘要：
We present a combinatorial model of configuration spaces and polytopes associated to the quotients of $\mathbb{C} A_n$, the path algebra of the linearly oriented $A_n$ quiver, i.e. the algebra of upper triangular matrices. These quotient algebras are known as linear Nakayama algebras. Such configuration spaces were recently introduced for more general algebras by the second author and collaborators. In this special setting, we provide elementary proofs and explicit combinatorial constructions. From a Dyck path we define three related objects: a finite-dimensional algebra, an affine algebraic variety, and a polytope. Moreover, our constructions are natural: each relation in the poset of Dyck paths gives a morphism between the corresponding objects.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
