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arXiv · 2409.01865

Cup product, Frölicher-Nijenhuis bracket and the derived bracket associated to Hom-Lie algebras

Anusuiya Baishya·Apurba Das
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Abstract

In this paper, we introduce some new graded Lie algebras associated with a Hom-Lie algebra. At first, we define the cup product bracket and its application to the deformation theory of Hom-Lie algebra morphisms. We observe an action of the well-known Hom-analogue of the Nijenhuis-Richardson graded Lie algebra on the cup product graded Lie algebra. Using the corresponding semidirect product, we define the Frölicher-Nijenhuis bracket and study its application to Nijenhuis operators. We show that the Nijenhuis-Richardson graded Lie algebra and the Frölicher-Nijenhuis algebra constitute a matched pair of graded Lie algebras. Finally, we define another graded Lie bracket, called the derived bracket that is useful to study Rota-Baxter operators on Hom-Lie algebras.

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Anusuiya Baishya, Apurba Das. 2024-09-03. Cup product, Frölicher-Nijenhuis bracket and the derived bracket associated to Hom-Lie algebras. https://arxiv.org/abs/2409.01865

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