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Algebra and Logic

, Volume 58, Issue 1, pp 1–14 | Cite as

Universal Enveloping Lie Rota–Baxter Algebras of Pre-Lie and Post-Lie Algebras

  • V. Yu. GubarevEmail author
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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 (RBλLie, 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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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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