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 $\mathcal{O}$-operator on bimodules over associative conformal algebras, we introduce the notion of $\mathcal{O}N$-structure on bimodules over associative conformal algebras and consider the relationship between it and the compatibility of $\mathcal{O}$-operators, the PN-structure, the $\Omega N$-structure and the $P\Omega$-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 $\mathcal{O}N$-structure, and an $\mathcal{O}N$-structure satisfying certain conditions gives a solution of the strong Maurer-Cartan equation of an associative conformal twilled algebra.

Keywords:

• Associative conformal algebra
• Maurer-Cartan equation
• Nijenhuis operator
• $\mathcal{O}$-operator

2020 Mathematics Subject Classification:

• 17A30
• 16S80
• 16D20

Acknowledgments

The authors are indebted to the referee for his/her help comments and suggestions which have improved the article.

Additional information

Funding

This work was financially supported by National Natural Science Foundation of China (No. 11771122, 11801141, 12201182), China Postdoctoral Science Foundation (2020M682272) and NSF of Henan Province (212300410120).