Quivers with potentials for Grassmannian cluster algebras

Abstract We consider a quiver with potential (QP) $(Q(D),W(D))$ and an iced (IQP) $(\overline {Q}(D), F(D), \overline {W}(D))$ associated Postnikov Diagram D prove that their mutations are compatible the geometric exchanges of . This ensures we may define QP $(Q,W)$ IQP {Q},F,\overline {W})$ for Grassmannian cluster algebra up to mutation equivalence. It shows is always rigid (thus nondegenerate) Jacobi-finite. Moreover, in fact, show it unique nondegenerate rigid) by using general result Geiß, Labardini-Fragoso, Schröer (2016, Advances Mathematics 290, 364–452). Then that, within class algebra, quivers determine potentials right As application, verify auto-equivalence group generalized category ${\mathcal {C}}_{(Q, W)}$ isomorphic automorphism ${{\mathcal {A}}_Q}$ trivial coefficients.