Extended $$\mathcal {O}$$-Operators, Novikov Yang-Baxter Equations and Post-Novikov Algebras

In this paper, we introduce the definition of extended \(\mathcal {O}\) -operators on a Novikov algebra \((A,\circ )\) associated to an A -bimodule Novikov algebra which is a generalization of the definition of \(\mathcal {O}\) -operators and show that there are new Novikov algebra structures on the A -bimodule Novikov algebra obtained from extended \(\mathcal {O}\) -operators. We also introduce the definition of post-Novikov algebras and show that there is a close relationship between post-Novikov algebras and \(\mathcal {O}\) -operators of weight \(\lambda\) . The tensor form of extended \(\mathcal {O}\) -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 \(\mathcal {O}\) -operators, Novikov Yang-Baxter equations, extended Novikov Yang-Baxter equations and generalized Novikov Yang-Baxter equations are established.