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arXiv · 2607.25246

Nijenhuis modules and the ring of Nijenhuis operators

Shilong Zhang·Xiao-Song Peng·Liuqing Dong
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Abstract

In this paper, we study the Nijenhuis modules of Nijenhuis algebras. The concepts of free, projective, injective, and flat Nijenhuis modules are introduced, and a construction of free Nijenhuis modules is given. The ring of Nijenhuis operators is introduced, and the relationship between Nijenhuis modules and modules over this ring is established by proving an isomorphism of the corresponding categories. Finally, it is proved that the category of Nijenhuis modules has enough projective, injective, and flat objects.

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BibTeXRIS

Shilong Zhang, Xiao-Song Peng, Liuqing Dong. 2026-07-28. Nijenhuis modules and the ring of Nijenhuis operators. https://arxiv.org/abs/2607.25246

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