Exploring Cohomology, Deformations, and Hom-NS Structures in Hom-Leibniz Conformal Algebras through Nijenhuis Operators
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913628904488960 |
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| author | Asif, Sania |
| author_facet | Asif, Sania |
| contents | This paper studies the Nijenhuis operator on Hom-Leibniz conformal algebra, defining their representations and cohomologies. We determine the cohomologies for both Hom-Leibniz conformal algebra and Nijenhuis operators on Hom-Leibniz conformal algebra. Subsequently, establishing the cohomology of Hom-Nijenhuis-Leibniz conformal algebras. As an application to this cohomology, we study formal deformations of the Nijenhuis operator on Hom-Leibniz conformal algebra. Additionally, we introduce Hom-NS-Leibniz conformal algebra and explore how various operators such as Rota-Baxter operator, Twisted Rota Baxter operator, and Nijenhuis operators can provide Hom-NS-Leibniz conformal algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring Cohomology, Deformations, and Hom-NS Structures in Hom-Leibniz Conformal Algebras through Nijenhuis Operators Asif, Sania Rings and Algebras Operator Algebras 11R52, 15A99, 17B67, 17B10 This paper studies the Nijenhuis operator on Hom-Leibniz conformal algebra, defining their representations and cohomologies. We determine the cohomologies for both Hom-Leibniz conformal algebra and Nijenhuis operators on Hom-Leibniz conformal algebra. Subsequently, establishing the cohomology of Hom-Nijenhuis-Leibniz conformal algebras. As an application to this cohomology, we study formal deformations of the Nijenhuis operator on Hom-Leibniz conformal algebra. Additionally, we introduce Hom-NS-Leibniz conformal algebra and explore how various operators such as Rota-Baxter operator, Twisted Rota Baxter operator, and Nijenhuis operators can provide Hom-NS-Leibniz conformal algebras. |
| title | Exploring Cohomology, Deformations, and Hom-NS Structures in Hom-Leibniz Conformal Algebras through Nijenhuis Operators |
| topic | Rings and Algebras Operator Algebras 11R52, 15A99, 17B67, 17B10 |
| url | https://arxiv.org/abs/2412.20428 |