Journal of Lie Theory

no. 1
Poincaré-Birkhoff-Witt Theorem for Pre-Lie and Post-Lie Algebras
Journal of Lie Theory, Volume 30 (2020) no. 1, pp. 223-238
We construct the universal enveloping preassociative and postassociative algebra for a pre-Lie and a post-Lie algebra, respectively. We show that the pairs (pre-Lie, pre-As) and (post-Lie, post-As) are Poincaré-Birkhoff-Witt-pairs; for the first this is a reproof of the result of V. Dotsenko and P. Tamaroff.
DOI: 10.5802/jolt.1112
Classification: 16W99,17D25
Keywords: Rota-Baxter operator, Groebner-Shirshov basis, pre-Lie algebra, post-Lie algebra, preassociative algebra, dendriform algebra, postassociative algebra 
@article{JOLT_2020_30_1_a12,
     author = {V. Gubarev},
     title = {Poincar\'e-Birkhoff-Witt {Theorem} for {Pre-Lie} and {Post-Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {223--238},
     year = {2020},
     volume = {30},
     number = {1},
     doi = {10.5802/jolt.1112},
     zbl = {1442.17014},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1112/}
}
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V. Gubarev. Poincaré-Birkhoff-Witt Theorem for Pre-Lie and Post-Lie Algebras. Journal of Lie Theory, Volume 30 (2020) no. 1, pp. 223-238. doi: 10.5802/jolt.1112

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