On the representability of actions of Leibniz algebras and Poisson algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917022943674368 |
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| author | Cigoli, Alan S. Mancini, Manuel Metere, Giuseppe |
| author_facet | Cigoli, Alan S. Mancini, Manuel Metere, Giuseppe |
| contents | In a recent paper, motivated by the study of central extensions of associative algebras, G. Janelidze introduces the notion of weakly action representable category. In this paper, we show that the category of Leibniz algebras is weakly action representable and we characterize the class of acting morphisms. Moreover, we study the representability of actions of the category of Poisson algebras by describing explicitly a universal strict general actor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_05175 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the representability of actions of Leibniz algebras and Poisson algebras Cigoli, Alan S. Mancini, Manuel Metere, Giuseppe Category Theory Rings and Algebras 08C05, 18E13, 17A32, 17B63, 16B50, 17A36, 16W25 In a recent paper, motivated by the study of central extensions of associative algebras, G. Janelidze introduces the notion of weakly action representable category. In this paper, we show that the category of Leibniz algebras is weakly action representable and we characterize the class of acting morphisms. Moreover, we study the representability of actions of the category of Poisson algebras by describing explicitly a universal strict general actor. |
| title | On the representability of actions of Leibniz algebras and Poisson algebras |
| topic | Category Theory Rings and Algebras 08C05, 18E13, 17A32, 17B63, 16B50, 17A36, 16W25 |
| url | https://arxiv.org/abs/2302.05175 |