Journal of Lie Theory

no. 2
Lie Elements in Pre-Lie Algebras, Trees and Cohomology Operations
Journal of Lie Theory, Volume 17 (2007) no. 2, pp. 241-261
We give a simple characterization of Lie elements in free pre-Lie algebras as elements of the kernel of a map between spaces of trees. We explain how this result is related to natural operations on the Chevalley-Eilenberg complex of a Lie algebra. We also indicate a possible relation to Loday's theory of triplettes.
DOI: 10.5802/jolt.445
Classification: 17B01, 17B56
Keywords: Cohomology operations, pre-Lie algebras, Chevalley-Eilenberg complex 
@article{JOLT_2007_17_2_a1,
     author = {M. Markl},
     title = {Lie {Elements} in {Pre-Lie} {Algebras,} {Trees} and {Cohomology} {Operations}},
     journal = {Journal of Lie Theory},
     pages = {241--261},
     year = {2007},
     volume = {17},
     number = {2},
     doi = {10.5802/jolt.445},
     zbl = {1123.17006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.445/}
}
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%J Journal of Lie Theory
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M. Markl. Lie Elements in Pre-Lie Algebras, Trees and Cohomology Operations. Journal of Lie Theory, Volume 17 (2007) no. 2, pp. 241-261. doi: 10.5802/jolt.445

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