Connes-kreimer Quantizations and Pbw Theorems for Pre-lie Algebras
نویسنده
چکیده
The Connes-Kreimer renormalization Hopf algebras are examples of a canonical quantization procedure for pre-Lie algebras. We give a simple construction and explanation of this quantization using the universal enveloping algebra for so-called twisted Lie algebras (Lie algebras in the category of symmetric sequences of k-modules). As an application, we obtain a simple proof of the (strengthened) PBW theorem for Lie algebras which come from a pre-Lie product (over an arbitrary commutative ring), and give generalizations.
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