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 author