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arXiv · 1901.08768

Frobenius algebras and root systems: the trigonometric case

Dali Shen
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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.

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Dali Shen. 2019-01-25. Frobenius algebras and root systems: the trigonometric case. https://arxiv.org/abs/1901.08768

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