Journal of Lie Theory

no. 2
Some Results on Quasi-Trace Functions on (Pre-)Lie Algebras
Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 413-430
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.
DOI: 10.5802/jolt.1236
Classification: 17A42, 17A60,17B38,17B56
Keywords: 3-Lie algebra, quasi-trace function, relative Rota-Baxter operator, symplectic structure, cohomology 
@article{JOLT_2022_32_2_a4,
     author = {M. Chen and Q. Wang and S. Xu},
     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},
     doi = {10.5802/jolt.1236},
     zbl = {1503.17008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1236/}
}
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M. Chen; Q. Wang; S. Xu. Some Results on Quasi-Trace Functions on (Pre-)Lie Algebras. Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 413-430. doi: 10.5802/jolt.1236

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