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arXiv · 2212.13600

On Ternary $F$-manifold Algebras and their Representations

A. Ben Hassine·T. Chtioui·M. Elhamdadi·S. Mabrouk
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Abstract

We introduce a notion of ternary $F$-manifold algebras which is a generalization of $F$-manifold algebras. We study representation theory of ternary $F$-manifold algebras. In particular, we introduce a notion of dual representation which requires additional conditions similar to the binary case. We then establish a notion of a coherence ternary $F$-manifold algebra. Moreover, we investigate the construction of ternary $F$-manifold algebras using $F$-manifold algebras. Furthermore, we introduce and investigate a notion of a relative Rota-Baxter operator with respect to a representation and use it to construct ternary pre-$F$-manifold algebras.

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BibTeXRIS

A. Ben Hassine, T. Chtioui, M. Elhamdadi, S. Mabrouk. 2022-12-27. On Ternary $F$-manifold Algebras and their Representations. https://arxiv.org/abs/2212.13600

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