Relative Rota-Baxter operators on Hom-Lie triple systems

Abstract

In this paper, we first introduce the notion of relative Rota-Baxter operators on Hom-Lie triple systems and define a cohomology of relative Rota-Baxter operators on Hom-Lie triple systems with coefficients in a suitable representation. Furthermore, we introduce and study Hom-pre-Lie triple systems as the underlying structure of relative Rota-Baxter operators on Hom-Lie triple systems. Finally, we provide relationships between relative Rota-Baxter operators on Hom-Lie algebras and associated Hom-Lie triple systems.

KEYWORDS:

• Cohomology
• Hom-Lie algebra
• Hom-Lie triple system
• Hom-pre-Lie triple system
• relative Rota-Baxter operator

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17A30
• 17B56
• 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).