Non-abelian cohomology of Nijenhuis Lie algebras and the inducibility of automorphisms and derivations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910840966348800 |
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| author | Das, Apurba |
| author_facet | Das, Apurba |
| contents | In this paper, we first introduce the non-abelian cohomology group of a Nijenhuis Lie algebra with values in another Nijenhuis Lie algebra and show that it parametrizes the isomorphism classes of all non-abelian extensions. In particular, we obtain a classification result for abelian extensions of a Nijenhuis Lie algebra by a given Nijenhuis representation. Next, given a non-abelian extension of Nijenhuis Lie algebras, we investigate the inducibility of a pair of Nijenhuis Lie algebra automorphisms and show that the corresponding obstruction lies in the non-abelian cohomology group. Subsequently, we also consider the inducibility of a pair of Nijenhuis Lie algebra derivations in a given abelian extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-abelian cohomology of Nijenhuis Lie algebras and the inducibility of automorphisms and derivations Das, Apurba Rings and Algebras K-Theory and Homology 17B40, 17B55, 17B56 In this paper, we first introduce the non-abelian cohomology group of a Nijenhuis Lie algebra with values in another Nijenhuis Lie algebra and show that it parametrizes the isomorphism classes of all non-abelian extensions. In particular, we obtain a classification result for abelian extensions of a Nijenhuis Lie algebra by a given Nijenhuis representation. Next, given a non-abelian extension of Nijenhuis Lie algebras, we investigate the inducibility of a pair of Nijenhuis Lie algebra automorphisms and show that the corresponding obstruction lies in the non-abelian cohomology group. Subsequently, we also consider the inducibility of a pair of Nijenhuis Lie algebra derivations in a given abelian extension. |
| title | Non-abelian cohomology of Nijenhuis Lie algebras and the inducibility of automorphisms and derivations |
| topic | Rings and Algebras K-Theory and Homology 17B40, 17B55, 17B56 |
| url | https://arxiv.org/abs/2502.16254 |