On Zinbiel and Tortkara superalgebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911106209939456 |
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| author | Bouarroudj, Sofiane Mashurov, Farukh |
| author_facet | Bouarroudj, Sofiane Mashurov, Farukh |
| contents | In this paper, we study Zinbiel superalgebras and special Tortkara superalgebras, highlighting key differences between the super and the non-super setting. We present examples of Zinbiel superalgebras with Rota-Baxter operators and construct a basis for free Zinbiel superalgebras. Moreover, we establish a superalgebraic analogue of the Lie criterion for Zinbiel superalgebras. In contrast to the classical case, some homomorphic images of special Tortkara superalgebras on two generators are exceptional. Finally, we present a classification of all Tortkara superalgebras of dimensions 2 and 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Zinbiel and Tortkara superalgebras Bouarroudj, Sofiane Mashurov, Farukh Rings and Algebras 17A30, 17A50, 17A70 In this paper, we study Zinbiel superalgebras and special Tortkara superalgebras, highlighting key differences between the super and the non-super setting. We present examples of Zinbiel superalgebras with Rota-Baxter operators and construct a basis for free Zinbiel superalgebras. Moreover, we establish a superalgebraic analogue of the Lie criterion for Zinbiel superalgebras. In contrast to the classical case, some homomorphic images of special Tortkara superalgebras on two generators are exceptional. Finally, we present a classification of all Tortkara superalgebras of dimensions 2 and 3. |
| title | On Zinbiel and Tortkara superalgebras |
| topic | Rings and Algebras 17A30, 17A50, 17A70 |
| url | https://arxiv.org/abs/2508.11382 |