On the mutation loops of valued quivers

• Date: 2023
• Main Author: Saleh, I.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: cluster algebras; global mutation loops; Primary 13F60; Secondary 05E15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2083
• Journal Title: Algebra and Discrete Mathematics

A mutation loop of a valued quiver, \(Q\), is a combination of quiver automorphisms and mutations that sends \(Q\)  to itself. Moreover, it will be called symmetric if it sends \(Q\) to \(\epsilon\sigma(Q)\), \(\epsilon \in \{-1, 1\}\) for some permutation \(\sigma\). A global mutation loop of \(Q\)...