Geodesic
Some Results on Quasi-Trace Functions on (Pre-)Lie Algebras
Ming Chen1 ; Qi Wang2 ; Senrong Xu3
1School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, P. R. China
2School of Mathematics and Statistics, Changchun University of Technology, Changchun, Jilin, P. R. China
3Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, P. R. China
Journal of Lie Theory, Tome 32 (2022) no. 2, pp. 413-430

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17A42, 17A60,17B38,17B56
Mots-clés : 3-Lie algebra, quasi-trace function, relative Rota-Baxter operator, symplectic structure, cohomology

Ming Chen  1   ; Qi Wang  2   ; Senrong Xu  3

1 School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, P. R. China
2 School of Mathematics and Statistics, Changchun University of Technology, Changchun, Jilin, P. R. China
3 Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, P. R. China 
Ming Chen; Qi Wang; Senrong Xu. Some Results on Quasi-Trace Functions on (Pre-)Lie Algebras. Journal of Lie Theory, Tome 32 (2022) no. 2, pp. 413-430. http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a4/
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     title = {Some {Results} on {Quasi-Trace} {Functions} on {(Pre-)Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {413--430},
     year = {2022},
     volume = {32},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a4/}
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