We study cluster tilting modules in mesh algebras of Dynkin type as defined in [12], providing a new proof for their existence. Except for type ${\mathbb{G}}_2$, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain automorphism. We further study their mutation, providing an example of mutation in an abelian category which is not stably 2-Calabi-Yau, and explicitly describe the combinatorics.

中文翻译：

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网格代数的集群倾斜模块

我们研究了 [12] 中定义的 Dynkin 类型网格代数中的集群倾斜模块，为它们的存在提供了新的证明。除了类型${\mathbb{G}}_2$，我们证明这些正是最大刚性模块，并且它们对于某个自同构是等变的。我们进一步研究了它们的突变，提供了一个在不稳定的 2-Calabi-Yau 的阿贝尔范畴中突变的例子，并明确描述了组合。