Kupershmidt operators on $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras structures
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912102866747392 |
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| author | Ncib, Othmen Silvestrov, Sergei |
| author_facet | Ncib, Othmen Silvestrov, Sergei |
| contents | The purpose of this paper is to introduce the class of noncommutative $3$-BiHom-Poisson color algebras, which is a combination of $3$-BiHom-Lie color algebras and BiHom-associative color algebras under a compatibility condition, called BiHom-Leibniz color identity, and then study their representations and associated Kupershmidt operators. In addition, we introduce the notion of noncommutative $3$-BiHom-pre-Poisson color algebras and investigate the relationship between noncommutative $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras via Kupershmidt operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kupershmidt operators on $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras structures Ncib, Othmen Silvestrov, Sergei Rings and Algebras 17B61, 17D30 (Primary) 17A30, 17A40, 17B63, 17B75 (Secondary) The purpose of this paper is to introduce the class of noncommutative $3$-BiHom-Poisson color algebras, which is a combination of $3$-BiHom-Lie color algebras and BiHom-associative color algebras under a compatibility condition, called BiHom-Leibniz color identity, and then study their representations and associated Kupershmidt operators. In addition, we introduce the notion of noncommutative $3$-BiHom-pre-Poisson color algebras and investigate the relationship between noncommutative $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras via Kupershmidt operators. |
| title | Kupershmidt operators on $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras structures |
| topic | Rings and Algebras 17B61, 17D30 (Primary) 17A30, 17A40, 17B63, 17B75 (Secondary) |
| url | https://arxiv.org/abs/2411.01413 |