
Journal of Lie Theory 32 (2022), No. 2, 413430 Copyright Heldermann Verlag 2022 Some Results on QuasiTrace 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 RotaBaxter operators and the cohomology theory of Lie algebras and the 3Lie algebras induced by Lie algebras with quasitrace functions. We introduce a notion of a quasitrace function on a preLie algebra, which can be used to construct a 3preLie algebra. The relationships between symplectice structures, relative RotaBaxter operators and quasitrace functions on (pre) Lie algebras are discussed. Keywords: 3Lie algebra, quasitrace function, relative RotaBaxter operator, symplectic structure, cohomology. MSC: 17A42, 17A60,17B38,17B56. [ Fulltextpdf (155 KB)] for subscribers only. 