On Ternary $F$-manifold Algebras and their Representations

Autor:	Hassine, A. Ben, Chtioui, T., Elhamdadi, M., Mabrouk, S.
Rok vydání:	2022
Předmět:	Mathematics - Rings and Algebras 17B10 17B56 17A42
Druh dokumentu:	Working Paper
Popis:	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. Comment: Comments are welcome. arXiv admin note: text overlap with arXiv:2102.05595; text overlap with arXiv:2002.10238 by other authors
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.13600 Zobrazit plný text záznamu View this record from Arxiv