On Rota-Baxter and Nijenhuis anti-flexible algebras

TL;DR

This paper explores Rota-Baxter and Nijenhuis operators on anti-flexible algebras, establishing their properties and how they generate related algebraic structures like pre-anti-flexible and left-symmetric algebras.

Contribution

It introduces Rota-Baxter and Nijenhuis operators on anti-flexible algebras, and constructs associated algebraic structures, expanding the theoretical framework of anti-flexible algebra theory.

Findings

Defined Rota-Baxter operator on anti-flexible algebra

Constructed pre-anti-flexible and left-symmetric algebras from Rota-Baxter operators

Introduced Nijenhuis anti-flexible algebra and related properties

Abstract

We define and derive basic properties of the notion of Rota-Baxter operator on anti-flexible algebra. Starting from a Rota-Baxter operator on an anti-flexible algebra, we construct pre-anti-flexible algebra structure and associated left(right)-symmetric algebra as well. The notion of O-operator on anti-flexible algebra is recalled and used to build left(right)- symmetric algebra as well as related properties. Furthermore, we introduce Nijenhuis anti-flexible algebra and derive associated properties. Nijenhuis operator on anti-flexible algebra is used to build pre-anti-flexible algebra structure and related left(right)-symmetric algebra.