Frobenius manifolds from subregular classical W-algebras

2011/08/27 by Yassir Dinar, Dinar, Yassir · 2 citations
Mathematics · Physics and Astronomy · #14B07 #17B80 #37K25 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.AG #math.DG #math.MP #msc:14B07 #msc:17B80 #msc:37K25 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1108.5445

26 pages, 3 tables

arxiv created 2011/08/27 · openalex publication_date 2011/08/27 · arxiv updated 2011/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• From Adler-Gelfand-Dickey Brackets to Logarithmic Dubrovin-Frobenius manifolds
• The quadratic WDVV solution E₈(a₁)

Related

• Algebraic classical W-algebras and Frobenius manifolds
• Free frobenius algebra on the differential forms of a manifold
• Geometry and analytic theory of Frobenius manifolds
• Weak Frobenius manifolds
• tt* geometry, Frobenius manifolds, their connections, and the\n construction for singularities