# Frobenius algebras and root systems: the trigonometric case

## TL;DR

This paper constructs Frobenius structures on certain bundles related to root systems, leading to a new class of Frobenius manifolds with explicit potential functions, extending algebraic structures into the trigonometric setting.

## Contribution

It introduces a novel construction of Frobenius structures on toric arrangement complements associated with root systems, creating a trigonometric version of Frobenius algebras and manifolds.

## Key findings

- Construction of Frobenius structures on $\
- $ ext{C}^ imes$-bundles related to root systems.
- Introduction of a trigonometric version of Frobenius algebras and manifolds.

## Abstract

We construct Frobenius structures on the $\mathbb{C}^{\times}$-bundle of the complement of a toric arrangement associated with a root system, by making use of a one-parameter family of torsion free and flat connections on it. This gives rise to a trigonometric version of Frobenius algebras in terms of root systems and a new class of Frobenius manifolds. We also determine their potential functions.