Gijs Heuts

Poincaré–Birkhoff–Witt theorems in higher algebra

We extend the classical Poincaré-Birkhoff-Witt (PBW) theorem to higher algebra by establishing a version that applies to spectral Lie algebras. We deduce this statement from a basic relation between operads in spectra: the commutative operad is the quotient of the associative ope...