On Ternary $F$-manifold Algebras and their Representations

A. Ben Hassine; T. Chtioui; M. Elhamdadi; S. Mabrouk

On Ternary $F$-manifold Algebras and their Representations

Rings and Algebras 2022-12-29 v1

Authors: A. Ben Hassine , T. Chtioui , M. Elhamdadi , S. Mabrouk

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.

Keywords

ternary F-manifold algebra representation theory dual representation coherence ternary F-manifold algebra relative Rota-Baxter operator ternary pre-F-manifold algebra

Cite

@article{arxiv.2212.13600,
  title  = {On Ternary $F$-manifold Algebras and their Representations},
  author = {A. Ben Hassine and T. Chtioui and M. Elhamdadi and S. Mabrouk},
  journal= {arXiv preprint arXiv:2212.13600},
  year   = {2022}
}

Comments

Comments are welcome. arXiv admin note: text overlap with arXiv:2102.05595; text overlap with arXiv:2002.10238 by other authors

On Ternary $F$-manifold Algebras and their Representations

Abstract

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