In this paper, we construct a bialgebra theory for associative conformal algebras, namely antisymmetric infinitesimal conformal bialgebras. On the one hand, it is an attempt to give conformal structures for antisymmetric infinitesimal bialgebras. On the other hand, under certain conditions, such structures are equivalent to double constructions of Frobenius conformal algebras, which are associative conformal algebras that are decomposed into the direct sum of another associative conformal algebra and its conformal dual as $\mathbb{C}[\partial ]$-modules such that both of them are subalgebras and the natural conformal bilinear form is invariant. The coboundary case leads to the introduction of associative conformal Yang-Baxter equation whose antisymmetric solutions give antisymmetric infinitesimal conformal bialgebras. Moreover, the construction of antisymmetric solutions of associative conformal Yang-Baxter equation is given from $\mathcal{O}$-operators of associative conformal algebras as well as dendriform conformal algebras.

在本文中，我们构造了结合共形代数的双代数理论，即反对称无穷小共形双代数。一方面，它试图给出反对称无穷小双代数的共形结构。另一方面，在一定条件下，这样的结构等价于 Frobenius 保形代数的双重构造，即结合保形代数分解为另一个结合保形代数及其保形对偶的直和为$\mathbb{C}[\partial ]$-modules 使得它们都是子代数并且自然的共形双线性形式是不变的。共边界情况导致引入了结合共形 Yang-Baxter 方程，其反对称解给出了反对称无穷小共形双代数。此外，结合共形Yang-Baxter方程的反对称解的构造由下式给出$\mathcal{哦}$-结合共形代数和树状共形代数的算子。