Journal of Lie Theory 32 (2022), No. 2, 413--430
Copyright Heldermann Verlag 2022
Some Results on Quasi-Trace Functions on (Pre-)Lie Algebras
Ming Chen
School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, P. R. China
chenm468@nenu.edu.cn
Qi Wang
School of Mathematics and Statistics, Changchun University of Technology, Changchun, Jilin, P. R. China
wangqi2018@ccut.edu.cn
Senrong Xu
Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, P. R. China
senrongxu@ujs.edu.cn
The aim of this paper is to compare the representations, symplectic structures, relative Rota-Baxter operators and the cohomology theory of Lie algebras and the 3-Lie algebras induced by Lie algebras with quasi-trace functions. We introduce a notion of a quasi-trace function on a pre-Lie algebra, which can be used to construct a 3-pre-Lie algebra. The relationships between symplectice structures, relative Rota-Baxter operators and quasi-trace functions on (pre-) Lie algebras are discussed.
Keywords: 3-Lie algebra, quasi-trace function, relative Rota-Baxter operator, symplectic structure, cohomology.
MSC: 17A42, 17A60,17B38,17B56.
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