The constructions and deformations of Nijenhuis operators on 3-Hom-Lie algebras

Yizheng Li; Dingguo Wang

doi:10.4134/JKMS.j230612

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2025; 62(1): 127-143

Online first article December 18, 2024 Printed January 1, 2025

https://doi.org/10.4134/JKMS.j230612

The constructions and deformations of Nijenhuis operators on 3-Hom-Lie algebras

Yizheng Li; Dingguo Wang

Qufu Normal University; Qufu Normal University

Abstract

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Abstract

In this paper, we study Nijenhuis operators on 3-Hom-Lie algebras and provide some examples. Next, we give various constructions of Nijenhuis operators according to constructions of 3-Hom-Lie algebras. Furthermore, we define a cohomology of Nijenhuis operators on 3-Hom-Lie algebras with coefficients in a suitable representation. Finally, as an application, we study formal deformations of Nijenhuis operators that are generated by the above-defined cohomology.

Keywords: Nijenhuis operator, Rota-Baxter operator, cohomology, formal deformation

MSC numbers: Primary 17A30, 17B60, 17B61

Supported by: This work was financially supported by the NSF of China (No. 12271292).