Cohomology, Homotopy, Extensions, and Automorphisms of Nijenhuis Lie Conformal Algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916761722421248 |
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| author | Asif, Sania |
| author_facet | Asif, Sania |
| contents | This paper explores various algebraic and homotopical aspects of Nijenhuis Lie conformal algebras, including their cohomology theory, $\mathcal{L}_\infty$-structures, non-abelian extensions, and automorphism groups. We define the cohomology of a Nijenhuis Lie conformal algebra and relate it to the deformation theory of such structures. We also introduce $2$-term Nijenhuis $\mathcal{L}_\infty$-conformal algebras and establish their correspondence with crossed modules and $3$-cocycles in the cohomology of Nijenhuis Lie conformal algebras. Furthermore, we develop a classification theory for non-abelian extensions of Nijenhuis Lie conformal algebras via the second non-abelian cohomology group. Finally, we study the inducibility problem for automorphisms under such extensions, introducing a Wells-type map and deriving an associated exact sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20867 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohomology, Homotopy, Extensions, and Automorphisms of Nijenhuis Lie Conformal Algebras Asif, Sania Rings and Algebras 17B65, 17B10, 17B38, 17B69, 14F35, 18N10, 18N40 This paper explores various algebraic and homotopical aspects of Nijenhuis Lie conformal algebras, including their cohomology theory, $\mathcal{L}_\infty$-structures, non-abelian extensions, and automorphism groups. We define the cohomology of a Nijenhuis Lie conformal algebra and relate it to the deformation theory of such structures. We also introduce $2$-term Nijenhuis $\mathcal{L}_\infty$-conformal algebras and establish their correspondence with crossed modules and $3$-cocycles in the cohomology of Nijenhuis Lie conformal algebras. Furthermore, we develop a classification theory for non-abelian extensions of Nijenhuis Lie conformal algebras via the second non-abelian cohomology group. Finally, we study the inducibility problem for automorphisms under such extensions, introducing a Wells-type map and deriving an associated exact sequence. |
| title | Cohomology, Homotopy, Extensions, and Automorphisms of Nijenhuis Lie Conformal Algebras |
| topic | Rings and Algebras 17B65, 17B10, 17B38, 17B69, 14F35, 18N10, 18N40 |
| url | https://arxiv.org/abs/2505.20867 |