Embedding Tensors on 3-Hom-Lie Algebras
Received:May 03, 2023  Revised:August 14, 2023
Key Words: 3-Hom-Lie algebra   embedding tensor   representation   cohomology   deformation  
Fund Project: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) and the Doctoral Research Start-Up Fund of Guiyang University (Grant No.GYU-KY-2024).
Author NameAffiliation
Wen TENG School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China 
Jiulin JIN School of Science, Guiyang University, Guizhou 550005, P. R. China 
Yu ZHANG School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China 
Hits: 169
Download times: 130
Abstract:
      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.
Citation:
DOI:10.3770/j.issn:2095-2651.2024.02.005
View Full Text  View/Add Comment