English

Poincare-Birkhoff-Witt theorem for pre-Lie and postLie algebras

Rings and Algebras 2022-01-25 v1

Abstract

We construct the universal enveloping preassociative and postassociative algebra for a pre-Lie and a postLie algebra respectively. We show that the pairs (preLie,preAs)(\mathrm{preLie},\mathrm{preAs}) and (postLie,postAs)(\mathrm{postLie},\mathrm{postAs}) are Poincare-Birkhoff-Witt-pairs, for the first one it's a reproof of the result of V. Dotsenko and P. Tamaroff.

Keywords

Cite

@article{arxiv.1903.02960,
  title  = {Poincare-Birkhoff-Witt theorem for pre-Lie and postLie algebras},
  author = {Vsevolod Gubarev},
  journal= {arXiv preprint arXiv:1903.02960},
  year   = {2022}
}

Comments

17 p. arXiv admin note: text overlap with arXiv:1808.08839, arXiv:1808.09822