Twisted Rota-Baxter operators on 3-Hom-Lie algebras

Abstract

Abstract–In this paper, we first introduce the notion of twisted Rota-Baxter operators on 3-Hom-Lie algebras and define a cohomology of twisted Rota-Baxter operators on 3-Hom-Lie algebras with coefficients in a suitable representation. Furthermore, we introduce and study 3-Hom-NS-Lie-algebras as the underlying structure of twisted Rota-Baxter operators on 3-Hom-Lie algebras. Finally, we investigate twisted Rota-Baxter operators on 3-Hom-Lie algebras induced by Hom-Lie algebras.

Keywords:

• Cohomology
• Hom-NS-Lie algebra
• 3-Hom-NS-Lie algebra
• twisted Rota-Baxter operator

2020 Mathematics Subject Classification:

• 17A40
• 17B60
• 17B61

Acknowledgments

The authors would like to express their deep gratitude to the anonymous referee for a careful reading and valuable suggestions.

Additional information

Funding

The paper is supported by the NSF of China (No.12271292).