Singularities with Symmetries, orbifold Frobenius algebras and Mirror Symmetry

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dc.creatorKaufmann, Ralph M.
dc.date2003-12-22
dc.date2003-12-30
dc.date.accessioned2026-07-07T05:04:07Z
dc.date.available2026-07-07T05:04:07Z
dc.descriptionPreviously, 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 $B_n$ and $F_4$. Lastly, we relate our constructions to $r$ spin--curves, classical singularity theory and foldings of Dynkin diagrams.
dc.identifierhttps://arxiv.org/abs/math/0312417
dc.identifierhttp://arxiv.org/abs/math/0312417
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69682
dc.subjectAlgebraic Geometry
dc.subjectQuantum Algebra
dc.titleSingularities with Symmetries, orbifold Frobenius algebras and Mirror Symmetry
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