Kupershmidt-Nijenhuis structures on pre-Malcev algebras
Rings and Algebras
2025-12-15 v3
Abstract
We study Kupershmidt operators, Nijenhuis operators, and Kupershmidt-Nijenhuis structures on finite-dimensional pre-Malcev algebras over a field of characteristic zero. We construct several new families of complex pre-Malcev algebras that are not pre-Lie algebras in dimensions two, three and four. We use the compatibility of linear operators to establish connections between Kupershmidt operators, Nijenhuis operators, and Kupershmidt-Nijenhuis structures on pre-Malcev algebras. Moreover, we use a method from computational ideal theory to characterize the geometric structures of the varieties of Kupershmidt operators and Nijenhuis operators on a three-dimensional complex pre-Malcev algebra.
Keywords
Cite
@article{arxiv.2208.11841,
title = {Kupershmidt-Nijenhuis structures on pre-Malcev algebras},
author = {Yin Chen and Liman Qin and Shan Ren and Runxuan Zhang},
journal= {arXiv preprint arXiv:2208.11841},
year = {2025}
}
Comments
21 pages; To appear in Bull. Malays. Math. Sci. Soc