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Research Articles

The đť“žN-structure on bimodules over associative conformal algebras

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Pages 3074-3104 | Received 21 Apr 2022, Accepted 24 Jan 2023, Published online: 21 Feb 2023
 

Abstract

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

2020 Mathematics Subject Classification:

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).

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