Extended O-Operators, Novikov Yang-Baxter Equations and Post-Novikov Algebras

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. 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.