The 𝓞N-structure on bimodules over associative conformal algebras

Abstract

In this paper, we study the deformation theory of associative conformal algebras and conformal bimodules. Using the -operator on bimodules over associative conformal algebras, we introduce the notion of -structure on bimodules over associative conformal algebras and consider the relationship between it and the compatibility of -operators, the PN-structure, the -structure and the -structure on associative conformal algebra. We show that a solution of the strong Maurer-Cartan equation of an associative conformal twilled algebra gives rise to an -structure, and an -structure satisfying certain conditions gives a solution of the strong Maurer-Cartan equation of an associative conformal twilled algebra.