On classification and construction of algebraic Frobenius manifolds

DOI10.1016/j.geomphys.2008.04.001zbMath1149.53322arXiv0706.0960OpenAlexW2088310069MaRDI QIDQ950266

Yassir Ibrahim Dinar

Publication date: 22 October 2008

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.0960

zbMATH Keywords

integrable systemsbi-Hamiltonian manifoldsFrobenius manifoldsDirac reduction

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (53D45)

Related Items (max. 100)

Hurwitz numbers for reflection groups. II: Parabolic quasi-Coxeter elements ⋮ Frobenius manifolds from regular classical \(W\)-algebras ⋮ 4-dimensional Frobenius manifolds and Painlevé VI ⋮ The WDVV solution \(E_8(a_1)\) ⋮ Algebraic classical \(W\)-algebras and Frobenius manifolds ⋮ \(W\)-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions ⋮ Explicit examples of Hurwitz Frobenius manifolds in genus one ⋮ On integrability of transverse Lie-Poisson structures at nilpotent elements

Cites Work

• Reduction of Poisson manifolds
• Generalized Drinfel'd-Sokolov hierarchies
• Generalized Toda theories and \(\mathcal W\)-algebras associated with integral gradings
• Drinfeld-Sokolov reduction on a simple Lie algebra from the bihamiltonian point of view
• Bihamiltonian reductions and \({\mathcal W}_n\)-algebras
• Generalized Drinfel'd-Sokolov hierarchies. II: The Hamiltonian structures
• Regular elements of finite reflection groups
• Equivalence of the Drinfeld-Sokolov reduction to a bi-Hamiltonian reduction
• Toda theory and \({\mathcal W}\)-algebra from a gauged WZNW point of view
• Hurwitz action on tuples of Euclidean reflections.
• Regular conjugacy classes in the Weyl group and integrable hierarchies
• A note on fractional KdV hierarchies
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