类型$A_{2N}$的变形簇映射
Deformed cluster maps of type $A_{2N}$
AI总结：
研究类型$A_{2N}$的变形可积簇映射，构建高维映射并证明其整性，首次提出无限类例子，揭示离散可积系统的性质。
摘要：
我们扩展了第三作者与Kouloukas最近的工作，通过构造对应于Dynkin类型$A_{2N}$的可积簇映射的变形，将这些映射提升到更高维的映射中，这些映射具有Laurent性质，并证明对于$N\leq 3$的变形具有整性。这提供了首个无限类的例子（在任意高秩下），并提供了相关离散可积系统的信息。我们方法的关键是一种对quiver的『局部展开』操作，允许我们从类型$A_{2(N-1)}$的突变构造并研究类型$A_{2N}$的突变。
英文摘要：
We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types $A_{2N}$, lifting these to higher-dimensional maps possessing the Laurent property and demonstrating integrality of the deformations for $N\leq 3$. This provides the first infinite class of examples (in arbitrarily high rank) of such maps and gives information on the associated discrete integrable systems. Key to our approach is a ``local expansion'' operation on quivers which allows us to construct and study mutations in type $A_{2N}$ from those in type $A_{2(N-1)}$.
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。
