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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.12866 |
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| _version_ | 1866910494115233792 |
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| author | Harrathi, Fattoum |
| author_facet | Harrathi, Fattoum |
| contents | The purpose of this paper is to introduce the notion of pre-Malcev superalgebras as the algebraic structure behind the super $\mathcal{O}$-operators on Malcev superalgebras. Moreover, the relations among Malcev superalgebras, pre-Malcev superalgebras and pre-alternative superalgebras are established. Then, we study the operator forms of the classical Yang-Baxter equation (CYBE) in Malcev superalgebras and give their relationship with super $\mathcal{O}$-operators. There are close relationships between the CYBE in Malcev superalgebras and pre-Malcev superalgebras which can be interpreted through the super $\mathcal{O}$-operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Skew-supersymmetric solution of the super Malcev Yang-Baxter equation and Pre-Malcev superalgebras Harrathi, Fattoum Rings and Algebras The purpose of this paper is to introduce the notion of pre-Malcev superalgebras as the algebraic structure behind the super $\mathcal{O}$-operators on Malcev superalgebras. Moreover, the relations among Malcev superalgebras, pre-Malcev superalgebras and pre-alternative superalgebras are established. Then, we study the operator forms of the classical Yang-Baxter equation (CYBE) in Malcev superalgebras and give their relationship with super $\mathcal{O}$-operators. There are close relationships between the CYBE in Malcev superalgebras and pre-Malcev superalgebras which can be interpreted through the super $\mathcal{O}$-operators. |
| title | Skew-supersymmetric solution of the super Malcev Yang-Baxter equation and Pre-Malcev superalgebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2406.12866 |