Bialgebra theory and $\mathcal O$-operators of admissible Hom-Poisson algebras
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915256076337152 |
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| author | Benali, Karima |
| author_facet | Benali, Karima |
| contents | In this paper, we present and explore several key concepts within the framework of Hom-Poisson algebras. Specifically, we introduce the notions of admissible Hom-Poisson algebras, along with the related ideas of matched pairs and Manin triples for such algebras. We then define the concept of a purely admissible Hom-Poisson bialgebra, placing particular emphasis on its compatibility with the Manin triple structure associated with a nondegenerate symmetric bilinear form. This compatibility is crucial for understanding the structural interplay between these algebraic objects. Additionally, we investigate the notion of Hom-$ \mathcal O$-operators acting on admissible Hom-Poisson algebras. We analyze their properties and establish a connection with admissible Hom-pre-Poisson algebras, shedding light on the relationship between these two structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bialgebra theory and $\mathcal O$-operators of admissible Hom-Poisson algebras Benali, Karima Rings and Algebras 17B61, 16T10, 16T25, 17B63, 17B62 In this paper, we present and explore several key concepts within the framework of Hom-Poisson algebras. Specifically, we introduce the notions of admissible Hom-Poisson algebras, along with the related ideas of matched pairs and Manin triples for such algebras. We then define the concept of a purely admissible Hom-Poisson bialgebra, placing particular emphasis on its compatibility with the Manin triple structure associated with a nondegenerate symmetric bilinear form. This compatibility is crucial for understanding the structural interplay between these algebraic objects. Additionally, we investigate the notion of Hom-$ \mathcal O$-operators acting on admissible Hom-Poisson algebras. We analyze their properties and establish a connection with admissible Hom-pre-Poisson algebras, shedding light on the relationship between these two structures. |
| title | Bialgebra theory and $\mathcal O$-operators of admissible Hom-Poisson algebras |
| topic | Rings and Algebras 17B61, 16T10, 16T25, 17B63, 17B62 |
| url | https://arxiv.org/abs/2504.03645 |