We study a finite-dimensional algebra Λ from a Postnikov diagram D in a disk, obtained from the dimer algebra of Baur-King-Marsh by factoring out the ideal generated by the boundary idempotent. Thus, Λ is isomorphic to the stable endomorphism algebra of a cluster tilting module T ∈CM(B) introduced by Jensen-King-Su in order to categorify the cluster algebra structure of \(\mathbb {C}[\text {Gr}_{k}(\mathbb {C}^{n})]\). We show that Λ is self-injective if and only if D has a certain rotational symmetry. In this case, Λ is the Jacobian algebra of a self-injective quiver with potential, which implies that its truncated Jacobian algebras in the sense of Herschend-Iyama are 2-representation finite. We study cuts and mutations of such quivers with potential leading to some new 2-representation finite algebras.

中文翻译：

---

Postnikov图的自射雅可比代数

我们从磁盘中的Postnikov图D中研究了有限维代数Λ ，该代数是从Baur-King-Marsh的二聚体代数中获得的，它考虑了边界等幂线产生的理想值。因此，Λ是同构的一个簇倾斜模块的稳定的自同态代数Ť ∈CM（乙詹森景苏为了categorify的簇代数结构引入）\（\ mathbb {C} [\ {文本的Gr} _ {k}（\ mathbb {C} ^ {n}）] \）。我们证明当且仅当D具有一定的旋转对称性。在这种情况下，Λ是具有势能的自注射颤动的雅可比代数，这意味着从Herschend-Iyama的意义上来看，其截断的雅可比代数是2表示有限元。我们研究这种颤动的剪切和突变，并可能导致一些新的2表示有限代数。