On Rota-Baxter and Nijenhuis anti-flexible algebras
Mafoya Landry Dassoundo

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Algebraic structures and combinatorial models
