Deformations theory and minimal model of operads for Nijenhuis algebras morphisms
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912529898274816 |
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| author | Benabdelhafidh, Sami |
| author_facet | Benabdelhafidh, Sami |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformations theory and minimal model of operads for Nijenhuis algebras morphisms Benabdelhafidh, Sami Rings and Algebras 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. |
| title | Deformations theory and minimal model of operads for Nijenhuis algebras morphisms |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2508.06745 |