We obtain algebraic Frobenius manifolds from classical $W$-algebras associated to subregular nilpotent elements in simple Lie algebras of type $D_r$ where $r$ is even and $E_r$. The resulting Frobenius manifolds are certain hypersurfaces in the total spaces of semiuniversal deformation of simple hypersurface singularities of the same types.
- Pub Date:
- August 2011
- Mathematics - Differential Geometry;
- Mathematical Physics;
- Mathematics - Algebraic Geometry;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- 26 pages, 3 tables