Embedding Tensors on 3-Hom-Lie Algebras  

作　　者：Wen TENG Jiulin JIN Yu ZHANG 

机构地区：[1]School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guizhou 550025,P.R.China [2]School of Science,Guiyang University,Guizhou 550005,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第2期187-198,共12页数学研究及应用（英文版）

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;QKHZC[2023]372;ZK[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).

摘　　要：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.

关 键 词：3-Hom-Lie algebra embedding tensor representation COHOMOLOGY DEFORMATION 

分 类 号：O15[理学—数学]