On antisymmetric infinitesimal conformal bialgebras

$\mathcal{O}$-operators and Nijenhius operators of associative conformal algebras

“…Also, we gather some known results for later use. The material can be found in [18,21,28,29,32,33,36,37].…”

“…a matching pair of associative conformal algebras if A 1 and A 2 are subalgebras of A (cf. [29,31]). If an associative algebra decomposes into two subalgebras, it is also called an associative twilled algebra or simply twilled algebra in the literature (see, for example, [16]).…”

“…Proposition 2.6. ( [29]) Given an associative conformal algebra A and a conformal A -bimodule M, the vector space A ⊕ M carries an associative conformal algebra structure given by The associative conformal algebra from the proposition is called the semi-direct product algebra of A and M, and denoted by A ⊕ 0 M. It will be frequently used in this article.…”

“…We also introduce the notions of compatible O-operators and compatible dendriform conformal algebras and describe their interrelations. Let's start with recalling the definition of O-operators given in [29].…”

“…In the recent paper [29], Hong and Bai developed a bialgebra theory for associative conformal algebras, which can be viewed as a conformal analogue of associative bialgebras [3] and also as an associative analogue of conformal bialgebras [41]. In particular, they introduced the notions of O-operators of associative conformal algebras and dendriform conformal algebras to construct (antisymmetric) solutions of associative conformal Yang-Baxter equation.…”