On classification and construction of algebraic Frobenius manifolds

TL;DR

This paper develops a generalized bi-Hamiltonian reduction theory and applies it to loop algebras to construct new algebraic Frobenius manifolds, expanding the methods for their classification and construction.

Contribution

It introduces a generalized bi-Hamiltonian reduction framework and applies it to loop algebras to generate new algebraic Frobenius manifolds, extending existing construction techniques.

Findings

Recovered a generalized Drinfeld-Sokolov reduction

Constructed new algebraic Frobenius manifolds

Provided a systematic approach for classification

Abstract

We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to a suitable loop algebra we recover a generalized Drinfeld-Sokolov reduction. This gives a way to construct new examples of algebraic Frobenius manifolds.