TITLE: PBW in the wake of Poincaré
ABSTRACT: After a brief sketch of the historic background to Poincaréâs work on PBW [1900], we discuss in detail what moved Poincaré to invent the universal enveloping algebra, and how he approached the PBW problem, i.e., to exhibit a basis of the universal enveloping algebra. Then we outline some applications and developments in the direction laid out in Poincaréâs paper.