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arXiv · 2502.16254

Non-abelian cohomology of Nijenhuis Lie algebras and the inducibility of automorphisms and derivations

Apurba Das
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Abstract

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.

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Apurba Das. 2025-02-22. Non-abelian cohomology of Nijenhuis Lie algebras and the inducibility of automorphisms and derivations. https://arxiv.org/abs/2502.16254

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