Frobenius manifolds from regular classical $W$-algebras

TL;DR

This paper constructs polynomial Frobenius manifolds using classical W-algebras linked to regular nilpotent elements in simple Lie algebras, expanding the geometric understanding of these algebraic structures.

Contribution

It introduces a novel method to derive polynomial Frobenius manifolds from classical W-algebras associated with regular nilpotent elements.

Findings

Construction of polynomial Frobenius manifolds from classical W-algebras

Use of opposite Cartan subalgebras in the construction

New insights into the structure of Frobenius manifolds

Abstract

We obtain polynomial Frobenius manifolds from classical $W$-algebras associated to regular nilpotent elements in simple Lie algebras using the related opposite Cartan subalgebras.