2025/02/26 by Mabrouk, Sami, Silvestrov, Sergei, Zouaidi, Fatma · 1 citation
#17A40 #17B10 #17B56 #17B61 #17D30 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2502.18804
In this paper, we first introduce the notion of twisted \mathcal O-operators on a Hom-Lie-Yamaguti algebra by a given (2,3)-cocycle with coefficients in a representation. We show that a twisted \mathcal O-operator induces a Hom-Lie-Yamaguti structure. We also introduce the notion of a weighted Reynolds operator on a Hom-Lie-Yamaguti algebra, which can serve as a special case of twisted \mathcal O-operators on Hom-Lie-Yamaguti algebras. Then, we define a cohomology of twisted \mathcal O-operator on Hom-Lie-Yamaguiti algebras with coefficients in a representation. Furthermore, we introduce and study the Hom-NS-Lie-Yamaguti algebras as the underlying structure of the twisted \mathcal O-operator on Hom-Lie-Yamaguti algebras. Finally, we investigate the twisted \mathcal O-operator on Hom-Lie-Yamaguti algebras induced by the twisted \mathcal O-operator on a Hom-Lie algebras.