On Rota-Baxter and Nijenhuis anti-flexible algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915686921535488 |
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| author | Dassoundo, Mafoya Landry |
| author_facet | Dassoundo, Mafoya Landry |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_11834 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Rota-Baxter and Nijenhuis anti-flexible algebras Dassoundo, Mafoya Landry Rings and Algebras 17A30, 17B38 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. |
| title | On Rota-Baxter and Nijenhuis anti-flexible algebras |
| topic | Rings and Algebras 17A30, 17B38 |
| url | https://arxiv.org/abs/2207.11834 |