Embedding tensors on 3-Leibniz algebras and their derived algebraic structures and deformations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917915018657792 |
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| author | Teng, Wen Guo, Shuangjian |
| author_facet | Teng, Wen Guo, Shuangjian |
| contents | In this paper, first we introduce the notions of 3-tri-Leibniz algebras and embedding tensors on 3-Leibniz algebras. We show that an embedding tensor gives rise to a 3-tri-Leibniz algebra. Conversely, a 3-tri-Leibniz algebra gives rise to a 3-Leibniz algebra and a representation such that the quotient map is an embedding tensor. Furthermore, any 3-tri-Leibniz algebra can be embedded into an averaging 3-Leibniz algebra. Next, we introduce the notion of 3-tri-Leibniz dialgebras and demonstrate that homomorphic embedding tensors inherently induce 3-tri-Leibniz dialgebras. Finally, we study the linear deformations of embedding tensors by defining first cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04023 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embedding tensors on 3-Leibniz algebras and their derived algebraic structures and deformations Teng, Wen Guo, Shuangjian Rings and Algebras In this paper, first we introduce the notions of 3-tri-Leibniz algebras and embedding tensors on 3-Leibniz algebras. We show that an embedding tensor gives rise to a 3-tri-Leibniz algebra. Conversely, a 3-tri-Leibniz algebra gives rise to a 3-Leibniz algebra and a representation such that the quotient map is an embedding tensor. Furthermore, any 3-tri-Leibniz algebra can be embedded into an averaging 3-Leibniz algebra. Next, we introduce the notion of 3-tri-Leibniz dialgebras and demonstrate that homomorphic embedding tensors inherently induce 3-tri-Leibniz dialgebras. Finally, we study the linear deformations of embedding tensors by defining first cohomology. |
| title | Embedding tensors on 3-Leibniz algebras and their derived algebraic structures and deformations |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2502.04023 |