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Poincare-Birkhoff-Witt theorem for pre-Lie and postLie algebras
Published 6 Mar 2019 in math.RA | (1903.02960v1)
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.
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