Relative Rota-Baxter operators on Hom-Lie triple systems

AbstractIn 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: CohomologyHom-Lie algebraHom-Lie triple systemHom-pre-Lie triple systemrelative Rota-Baxter operator2020 MATHEMATICS SUBJECT CLASSIFICATION: 17A3017B5617B61 AcknowledgmentsThe authors would like to express their deep gratitude to the anonymous referee for a careful reading and valuable suggestions.Additional informationFundingThe paper is supported by the NSF of China (No.12271292).