Journal of Jilin University Science Edition ›› 2025, Vol. 63 ›› Issue (2): 353-0359.

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Generalized Reynolds Operators on Hom-Lie Algebras and Hom-NS-Lie Algebras

XU Senrong1, WANG Wei1, ZHAO Jia2   

  1. 1. School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu Province, China;  
    2. School of Sciences, Nantong University, Nantong 226019, Jiangsu Province, China
  • Received:2024-04-17 Online:2025-03-26 Published:2025-03-26

Abstract: Firstly, by providing  a Hom-Lie algebra and its representation,  we proved that a strong quasi-trace function on  a Hom-Lie algebra could induce a 3-Hom-Lie algebra and its representation, thereby proving that a generalized Reynolds operator on a Hom-Lie algebra was also  a generalized Reynolds operator on the  induced 3-Hom-Lie algebra. Secondly, we studied the mutual derivation properties of Hom-NS-Lie algebras and generalized Reynolds operators, and gave the adjoint relation of the corresponding categories.

Key words: Hom-Lie algebra, generalized Reynolds operator, 3-Hom-Lie algebra, Hom-NS-Lie algebra

CLC Number: 

  • O152.5