Relative (pre-)anti-flexible algebras and associated algebraic structures
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866909973951283200 |
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| author | Dassoundo, Mafoya Landry |
| author_facet | Dassoundo, Mafoya Landry |
| contents | Pre-anti-flexible family algebras are introduced and linked with the notions of relative anti-flexible algebras, left and right pre-Lie family algebras and relative Lie algebras which are for mostly newly defined. Relative pre-anti-flexible algebras are given and their underlying algebras structures such as pre-anti-flexible family algebras, left and right pre-Lie family algebras, and other are investigated and significant identities linking those introduced structures are derived. In addition, a generalization of the Rota-Baxter operators defined on a relative anti-flexible algebra is introduced and both Rota-Baxter operators and its generalization are used to build relative pre-anti-flexible algebras structures underlying relative anti-flexible algebras and related consequences are derived. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2011_05172 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Relative (pre-)anti-flexible algebras and associated algebraic structures Dassoundo, Mafoya Landry Rings and Algebras Combinatorics 17A30, 16W99, 05E16 Pre-anti-flexible family algebras are introduced and linked with the notions of relative anti-flexible algebras, left and right pre-Lie family algebras and relative Lie algebras which are for mostly newly defined. Relative pre-anti-flexible algebras are given and their underlying algebras structures such as pre-anti-flexible family algebras, left and right pre-Lie family algebras, and other are investigated and significant identities linking those introduced structures are derived. In addition, a generalization of the Rota-Baxter operators defined on a relative anti-flexible algebra is introduced and both Rota-Baxter operators and its generalization are used to build relative pre-anti-flexible algebras structures underlying relative anti-flexible algebras and related consequences are derived. |
| title | Relative (pre-)anti-flexible algebras and associated algebraic structures |
| topic | Rings and Algebras Combinatorics 17A30, 16W99, 05E16 |
| url | https://arxiv.org/abs/2011.05172 |