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arXiv · 2407.20033

The symmetric Poincar\'e-Birkhoff-Witt theorem and Dynkin-Magnus commutators

Gyula Lakos
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Abstract

The objective of this paper is to give alternative proofs for the symmetric Poincar\'e-Birkhoff-Witt theorem utilizing the Magnus recursion formulae or Dynkin's non-commutative polynomial comparison method and simple universal algebraic principles. As an application of these principles, a theorem of Nouaz\'e-Revoy type is also obtained.

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Gyula Lakos. 2024-07-29. The symmetric Poincar\'e-Birkhoff-Witt theorem and Dynkin-Magnus commutators. https://arxiv.org/abs/2407.20033

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