On some algebraic examples of Frobenius manifolds

TL;DR

This paper constructs explicit algebraic solutions to the WDVV equations using finite gap integration, extending these solutions to non-semisimple Frobenius manifolds.

Contribution

It introduces a novel analytical approach to generate algebraic solutions for Frobenius manifolds, including non-semisimple cases.

Findings

Explicit algebraic solutions to WDVV equations constructed

Solutions extended to non-semisimple Frobenius manifolds

Uses finite gap integration methods

Abstract

We construct some explicit quasihomogeneous algebraic solutions to the associativity (WDVV) equations by using analytical methods of the finite gap integration theory. These solutions are expanded in the uniform way to non-semisimple Frobenius manifolds.