### Poincaré’s proof of the co-called Birkhoff-Witt theorem

A methodical analysis of the research related to the article, “Sur les groupes continus”, of Henri Poincaré reveals many historical misconceptions and inaccuracies regarding his contribution to Lie theory. A thorough reading of this article confirms the priority of his discovery of many important concepts, especially that of the universal enveloping algebra of a Lie algebra over the real or complex field, and the canonical map (symmetrization) of the symmetric algebra onto the universal enveloping...