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 (preLie,preAs) and (postLie,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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