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

Abstract

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

arXiv comment17 p. arXiv admin note: text overlap with arXiv:1808.08839, arXiv:1808.09822