Nijenhuis modules and the ring of Nijenhuis operators

Shilong Zhang; Xiao-Song Peng; Liuqing Dong

Nijenhuis modules and the ring of Nijenhuis operators

Representation Theory 2026-07-28 v1 Rings and Algebras

Authors: Shilong Zhang , Xiao-Song Peng , Liuqing Dong

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.

Keywords

Nijenhuis algebras Nijenhuis modules Nijenhuis operators free modules projective modules injective modules flat modules category equivalence

Cite

@article{arxiv.2607.25246,
  title  = {Nijenhuis modules and the ring of Nijenhuis operators},
  author = {Shilong Zhang and Xiao-Song Peng and Liuqing Dong},
  journal= {arXiv preprint arXiv:2607.25246},
  year   = {2026}
}