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arXiv · 2208.11841

Kupershmidt-Nijenhuis structures on pre-Malcev algebras

Yin Chen·Liman Qin·Shan Ren·Runxuan Zhang
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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.

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Yin Chen, Liman Qin, Shan Ren, Runxuan Zhang. 2022-08-25. Kupershmidt-Nijenhuis structures on pre-Malcev algebras. https://doi.org/10.1007/s40840-025-02012-2

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