Weighted $\mathcal{O}$-operators on Hom-Lie triple systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908844696797184 |
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| author | Teng, Wen Jin, Jiulin |
| author_facet | Teng, Wen Jin, Jiulin |
| contents | In this paper, we first introduce the notion of a weighted $\mathcal{O}$-operator on Hom-Lie triple systems with respect to an action on another Hom-Lie triple system. Next, we construct a cohomology of weighted $\mathcal{O}$-operator on Hom-Lie triple systems, we use the first cohomology group to classify linear deformations and we investigate the obstruction class of an extendable $n$-order deformation. We end this paper by introducing a new algebraic structure, in connection with weighted $\mathcal{O}$-operators, called Hom-post-Lie triple system. We further show that Hom-post-Lie triple systems can be derived from Hom-post-Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13728 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weighted $\mathcal{O}$-operators on Hom-Lie triple systems Teng, Wen Jin, Jiulin Rings and Algebras 17A30, 17B38, 17B56, 17B61 In this paper, we first introduce the notion of a weighted $\mathcal{O}$-operator on Hom-Lie triple systems with respect to an action on another Hom-Lie triple system. Next, we construct a cohomology of weighted $\mathcal{O}$-operator on Hom-Lie triple systems, we use the first cohomology group to classify linear deformations and we investigate the obstruction class of an extendable $n$-order deformation. We end this paper by introducing a new algebraic structure, in connection with weighted $\mathcal{O}$-operators, called Hom-post-Lie triple system. We further show that Hom-post-Lie triple systems can be derived from Hom-post-Lie algebras. |
| title | Weighted $\mathcal{O}$-operators on Hom-Lie triple systems |
| topic | Rings and Algebras 17A30, 17B38, 17B56, 17B61 |
| url | https://arxiv.org/abs/2310.13728 |