Classification of connected étale algebras in pre-modular fusion categories up to rank three

We classify connected étale algebras $A$’s in pre-modular fusion categories $\mathcal{B}$ with $\text{rank}(\mathcal{B})\le 3$ including degenerate and non-(pseudo-)unitary ones. We comment on Lagrangian algebras and physical applications to ground state degeneracy and proof of spontaneous $\mathcal{B}$-symmetry breaking.