Singularities with Symmetries, orbifold Frobenius algebras and Mirror Symmetry

الأصل · EN

Previously, we introduced a duality transformation for Euler G--Frobenius algebras. Using this transformation, we prove that the simple A,D,E singularities and Pham singularities of coprime powers are mirror self--dual where the mirror duality is implemented by orbifolding with respect to the symmetry group generated by the grading operator and dualizing. We furthermore calculate orbifolds and duals to other G--Frobenius algebras which relate different G--Frobenius algebras for singularities. In particular, using orbifolding and the duality transformation we provide a mirror pairs for the simple boundary singularities Bₙ and F₄. Lastly, we relate our constructions to r spin--curves, classical singularity theory and foldings of Dynkin diagrams.