2003/12/22 by Ralph M. Kaufmann, Kaufmann, Ralph M.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.AG #math.QA
paper · pdf · doi:10.48550/arxiv.math/0312417
openalex publication_date 2003/12/22 · arxiv created 2003/12/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.