For Grassmannian cluster algebras, the non-degenerate quiver with potential is rigid and unique up to right-equivalence, and the auto-equivalence group of its category matches the cluster automorphism group.
Amiot, Cluster categories for algebras of global dimension 2 and quivers with potential
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Quivers with potentials for Grassmannian cluster algebras
For Grassmannian cluster algebras, the non-degenerate quiver with potential is rigid and unique up to right-equivalence, and the auto-equivalence group of its category matches the cluster automorphism group.