Algebra/Topology Seminar

Speaker: Pedro Tamaroff

Title: Poincaré--Birkhoff--Witt theorems: homotopical and effective computational methods for universal envelopes

Abstract: In joint work with V. Dotsenko, later extended to the dg setting in joint work with A. Khoroshkin, we developed a framework for studying Poincaré--Birkhoff--Witt type theorems about universal enveloping algebras of various algebraic structures, and used methods of term rewriting for operads to obtain new PBW theorems, answer an open question of J.-L. Loday, and study the universal enveloping functor of dg Lie algebras in the homotopy category. I will survey and explain the role homological algebra, homotopical algebra, and effective computational methods play in the main results obtained with both V. Dotsenko (1804.06485) and A. Khoroshikin (2003.06055) and, if time allows, explain a new direction in which these methods can be used to study certain operads as universal envelopes of pre-Lie algebras.