Geodesic
Universal enveloping Lie Rota–Baxter algebras of pre-Lie and post-Lie algebras
Algebra i logika, Tome 58 (2019) no. 1, pp. 3-21

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Universal enveloping Lie Rota–Baxter algebras of pre-Lie and post-Lie algebras are constructed. It is proved that the pairs of varieties (RBLie, preLie) and (RB$_\lambda$Lie, postLie) are PBW-pairs and that the variety of Lie Rota–Baxter algebras is not a Schreier variety.
Keywords: pre-Lie algebra, post-Lie algebra, Rota–Baxter algebra, uni­versal enveloping algebra, Lyndon–Shirshov word, PBW-pair of varieties, Schreier variety, partially commutative Lie algebra. 
@article{AL_2019_58_1_a0,
     author = {V. Yu. Gubarev},
     title = {Universal enveloping {Lie} {Rota{\textendash}Baxter} algebras of {pre-Lie} and {post-Lie} algebras},
     journal = {Algebra i logika},
     pages = {3--21},
     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_1_a0/}
}
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V. Yu. Gubarev. Universal enveloping Lie Rota–Baxter algebras of pre-Lie and post-Lie algebras. Algebra i logika, Tome 58 (2019) no. 1, pp. 3-21. http://geodesic.mathdoc.fr/item/AL_2019_58_1_a0/