Frobenius manifolds from regular classical \(W\)-algebras

DOI10.1016/j.aim.2010.12.024zbMath1216.37021arXiv1001.0611OpenAlexW2114418107MaRDI QIDQ633605

Yassir Ibrahim Dinar

Publication date: 29 March 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.0611

zbMATH Keywords

Frobenius manifoldsSlodowy slicebi-Hamiltonian geometryclassical \(W\)-algebrasDrinfeld-Sokolov reductionopposite Cartan subalgebra

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Simple, semisimple, reductive (super)algebras (17B20) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (53D45)

Related Items (5)

Hurwitz numbers for reflection groups. II: Parabolic quasi-Coxeter elements ⋮ 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 ⋮ Conjugate Frobenius manifold and inversion symmetry

Cites Work

• Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures
• On classification and construction of algebraic Frobenius manifolds
• Transverse Poisson structures to adjoint orbits in semisimple Lie algebras
• Generalized Toda theories and \(\mathcal W\)-algebras associated with integral gradings
• On the completeness of the set of classical \({\mathcal W}\)-algebras obtained from DS reductions
• Equivalence of the Drinfeld-Sokolov reduction to a bi-Hamiltonian reduction
• Toda theory and \({\mathcal W}\)-algebra from a gauged WZNW point of view
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• On a certain generator system of the ring of invariants of a finite reflection group
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