Journal of Jilin University Science Edition ›› 2021, Vol. 59 ›› Issue (6): 1375-1379.

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Generalized Derivation of Poisson 3-Lie Algebras

ZHANG Shuang1, WANG Chunyue2, ZHANG Qingcheng3   

  1. 1. Department of Basic Science, Jilin Jianzhu University, Changchun 130118, China;
    2. Faculty of Applied Sciences, Jilin Engineering Normal University, Changchun 130052, China;
    3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
  • Received:2021-03-01 Online:2021-11-26 Published:2021-11-26

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Abstract: By calculation, we gave some basic properties of the generalized derivation algebra GDer(L), quasiderivation algebra QDer(L), 
centroid C(L), quasicentroid QC(L) and central derivation algebra ZDer(L) of the Poisson 3-Lie algebras, and gave a necessary and sufficient condition that quasicentroid was a Lie algebra.

Key words: Poisson 3-Lie algebras, generalized derivation, quasiderivation, centroid

CLC Number: 

  • O152.5
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