2019/08/27 by Wen-Chang Chang, Jie Zhang, Chang, Wen +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1908.10103
openalex publication_date 2019/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider (iced) quiver with potential (Q(D), F(D), W(D)) associated to a Postnilov Diagram D and prove the mutation of the quiver with potential (\bareQ(D), F(D), W(D)) is compatible with the geometric exchange of the Postnikov diagram D. This ensures we may define a quiver with potential for a Grassmannian cluster algebra. We show such quiver with potential is always rigid (thus non-degenerate) and Jacobian-finite. And in fact, it is the unique non-degenerate (thus unique rigid) quiver with potential associated to the Grassmannian cluster algebra up to right-equivalence, by using a general result of Geiß-Labardini-Schröer. As an application, we verify that the auto-equivalence group of the generalized cluster category C(Q, W) is isomorphic to the cluster automorphism group of the associated Grassmannian cluster algebra A(Q, W) with trivial coefficients.