Reconstructing algebra objects from NIM-reps in pointed, near-group and quantum group-like fusion categories

Samuel Hannah, Ana Ros Camacho, with an appendix with Devi Young

In this article we study the possible Morita equivalence classes of algebras in three families of fusion categories (pointed, near-group and $A{\left(1,l\right)}_{\frac{1}{2}}$) b…