In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie...In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie algebras is defined.As an application,we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent,then their infinitesimals belong to the same cohomology class in the first cohomology group.展开更多
基金Supported by the Scientific Research Foundation for Science&Technology Innovation Talent Team of the Intelligent Computing and Monitoring of Guizhou Province(Grant No.QJJ[2023]063)the Science and Technology Program of Guizhou Province(Grant Nos.ZK[2023]025+4 种基金QKHZC[2023]372ZK[2022]031)the National Natural Science Foundation of China(Grant No.12161013)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022KYYB08)the Doctoral Research Start-Up Fund of Guiyang University(Grant No.GYU-KY-2024).
文摘In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie algebras is defined.As an application,we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent,then their infinitesimals belong to the same cohomology class in the first cohomology group.
