论文标题
关于三元$ f $ -manifold代数及其表示
On Ternary $F$-manifold Algebras and their Representations
论文作者
论文摘要
我们介绍了三元$ f $ -manifold代数的概念，该代数为$ f $ -manifold代数。我们研究三元$ f $ -manifold代数的代表理论。特别是，我们引入了双重表示的概念，该概念需要与二进制案例类似的其他条件。然后，我们建立了连贯的三元$ f $ -manifold代数的概念。此外，我们使用$ f $ -Manifold代数来研究三元$ f $ -manifold代数的构建。此外，我们介绍并研究了相对Rota-baxter操作员相对于表示形式的概念，并使用它来构建三元前$ f $ -Manifold代数。
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.
