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arXiv · 2508.06745

Deformations theory and minimal model of operads for Nijenhuis algebras morphisms

Sami Benabdelhafidh
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Abstract

Nijenhuis operators are very useful in the deformation theory of algebras. In this paper, we introduce a new cohomology theory related to deformation of Nijenhuis algebra morphisms, this notion involves simultaneous deformation of two Nijenhuis algebras and a morphism between them. As a consequence, we define a cohomology theory of Nijenhuis algebra morphisms to interpret the lower degree cohomology groups as formal deformation. We also prove a cohomology comparison Theorem of Nijenhuis algebra morphisms, i.e. the cohomology of a morphism of Nijenhuis algebras is isomorphic to the cohomology of an auxiliary Nijenhuis algebra. Finally, we construct a minimal model for the operad governing Nijenhuis algebras morphisms.

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Sami Benabdelhafidh. 2025-08-08. Deformations theory and minimal model of operads for Nijenhuis algebras morphisms. https://arxiv.org/abs/2508.06745

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