2025/05/27 by Yu, Jianfeng, Hong, Yanyong
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2505.20735
In this paper, we introduce the definition of extended O-operators on a Novikov algebra (A,∘) associated to an A-bimodule Novikov algebra which is a generalization of the definition of O-operators and show that there are new Novikov algebra structures on the A-bimodule Novikov algebra obtained from extended O-operators. We also introduce the definition of post-Novikov algebras and show that there is a close relationship between post-Novikov algebras and O-operators of weight λ. The tensor form of extended O-operators is also investigated which leads to the definition of extended Novikov Yang-Baxter equations, which is a generalization of the notion of Novikov Yang-Baxter equations. The relationships between extended O-operators, Novikov Yang-Baxter equations, extended Novikov Yang-Baxter equations and generalized Novikov Yang-Baxter equations are established.