Extended $\mathcal{O}$-operators, Novikov Yang-Baxter equations and post-Novikov algebras

TL;DR

This paper introduces extended $\\mathcal{O}$-operators on Novikov algebras, explores their connection to post-Novikov algebras, and generalizes Novikov Yang-Baxter equations, revealing new algebraic structures and relationships.

Contribution

It generalizes the concept of $\mathcal{O}$-operators to extended versions on Novikov algebras and links them to post-Novikov algebras and generalized Yang-Baxter equations.

Findings

Defined extended $\mathcal{O}$-operators on Novikov algebras.

Established relationships between extended $\mathcal{O}$-operators and generalized Yang-Baxter equations.

Connected post-Novikov algebras with $\mathcal{O}$-operators of weight $\lambda$.

Abstract

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.