Old and new aspects of the Poincaré-Birkhoff-Witt theorem
par
Vladimir DOTSENKO
→
Europe/Paris
112 (bât. Braconnier)
112
bât. Braconnier
ICJ, UCBL - La Doua
Description
The Poincaré-Birkhoff-Witt theorem on universal enveloping algebras of Lie algebras is a fundamental result in many areas of mathematics: from differential geometry and representation theory to homological algebra and deformation quantisation. I shall give a short overview of that result and some of its proofs that emerged in about 120 years since Poincaré published a paper about it, and outline a new proof which captures its category-theoretic essence in the best way possible, and allows to prove new similar theorems. The talk is based on a joint work with Pedro Tamaroff.
