| 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
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| 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). |
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| 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 |
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