Journal of Lie Theory 32 (2022), No. 2, 413--430
Copyright Heldermann Verlag 2022
Some Results on Quasi-Trace Functions on (Pre-)Lie Algebras
School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, P. R. China
School of Mathematics and Statistics, Changchun University of Technology, Changchun, Jilin, P. R. China
Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, P. R. China
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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