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arXiv · 2207.11834

On Rota-Baxter and Nijenhuis anti-flexible algebras

Mafoya Landry Dassoundo
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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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Mafoya Landry Dassoundo. 2022-07-24. On Rota-Baxter and Nijenhuis anti-flexible algebras. https://arxiv.org/abs/2207.11834

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