arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2311.03073math.COmath.ACmath.RA
收藏

Y型中楣图案

Y-frieze patterns

Antoine de Saint Germain

备注：
Some notation changed, Section 4 on the case of rank 2 added. The finiteness conjecture of v1 is now Theorem 5.5
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

簇系综的启发，我们引入了一个新的变种frieze模式相关的非循环簇代数，我们称之为${\bf Y}\textit{-frieze patterns}$。利用${\bf Y}$ -变量的突变规则，我们定义了一个大类的${\bf Y}$ -frieze模式，称为$\textit{unitary }{\bf Y}\textit{-frieze patterns}$，并证明了集合映射诱导了一个从（酉）frieze模式到（酉）${\bf Y}$ -frieze模式的映射.在秩2中，我们证明了${\bf Y}$ -frieze模式是广义簇代数的friezes。在有限型（不一定秩为2）下，我们证明了${\bf Y}$ -frieze模式与frieze模式具有相同的对称性，并证明了它们的个数是有限的.

英文摘要：

Motivated by cluster ensembles, we introduce a new variant of frieze patterns associated to acyclic cluster algebras, which we call ${\bf Y}\textit{-frieze patterns}$. Using the mutation rules for ${\bf Y}$-variables, we define a large class of ${\bf Y}$-frieze patterns called $\textit{unitary }{\bf Y}\textit{-frieze patterns}$, and show that the ensemble map induces a map from (unitary) frieze patterns to (unitary) ${\bf Y}$-frieze patterns. In rank 2, we show that ${\bf Y}$-frieze patterns are (associated to) friezes of generalised cluster algebras. In finite type (not necessarily rank 2), we show that ${\bf Y}$-frieze patterns share the same symmetries as frieze patterns, and prove that their number is finite.

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。

↑