Abstract:
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.
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