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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.00618 |
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| _version_ | 1866911938547548160 |
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| author | Mabrouk, Sami Ncib, Othmen |
| author_facet | Mabrouk, Sami Ncib, Othmen |
| contents | In this paper, we extend the concept of Lie superalgebras to a more generalized framework called Super-Lie superalgebras. In addition, they seem to be exploring various supergeneralizations of other algebraic structures, such as Super-associative, left (right) Super-Leibniz, and Super-left(right)-symmetric superalgebras, then we give some examples and related fundamental results. The notion of Rota-Baxter operators with any parity on the Super-Lie superalgebras is given. Moreover, we study a representations of Super-Lie superalgebras and its associate dual representations. The notion of derivations of Super-Lie superalgebras is introduced thus we show that the converse of a bijective derivation defines a Rota-Baxter operator. Finally, we give a generalization of the Super-Lie superalgebras and some other structures in the ternary case which we supported this with some examples and interesting results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Superalgebras with Homogeneous structures of Lie type Mabrouk, Sami Ncib, Othmen Rings and Algebras In this paper, we extend the concept of Lie superalgebras to a more generalized framework called Super-Lie superalgebras. In addition, they seem to be exploring various supergeneralizations of other algebraic structures, such as Super-associative, left (right) Super-Leibniz, and Super-left(right)-symmetric superalgebras, then we give some examples and related fundamental results. The notion of Rota-Baxter operators with any parity on the Super-Lie superalgebras is given. Moreover, we study a representations of Super-Lie superalgebras and its associate dual representations. The notion of derivations of Super-Lie superalgebras is introduced thus we show that the converse of a bijective derivation defines a Rota-Baxter operator. Finally, we give a generalization of the Super-Lie superalgebras and some other structures in the ternary case which we supported this with some examples and interesting results. |
| title | Superalgebras with Homogeneous structures of Lie type |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2407.00618 |