An isomorphism extension theorem for Landau-Ginzburg B-models

Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial W and a related symmetry group G. Given two polynomials W₁, W₂ with the same weights and same group G, the corresponding A-models built with (W₁,G) and (W₂,G) are isomorphic. Though the same result cannot hold in full generality for B-models, which correspond to orbifolded Milnor rings, we provide a partial analogue. In particular, we exhibit conditions where isomorphisms between unorbifolded B-models (or Milnor rings) can extend to isomorphisms between their corresponding orbifolded B-models (or orbifolded Milnor rings).