Frobenius manifolds from regular classical \(W\)-algebras (Q633605)

In the present paper the polynomial Frobenius manifolds are considered. They were obtained from classical \(W\)-algebras associated to regular nilpotent elements in simple Lie algebras using the related opposite Cartan subalgebras. This work consists of the following basic parts: Frobenius manifolds and local bi-Hamiltonian structures; regular nilpotent element and opposite Cartan subalgebra; Drinfeld-Sokolov reduction, the nondegeneracy condition and differential relation; some results from Dirac reduction; polynomial Frobenius manifold.