The universal enveloping algebra of a Lie algebra plays a key role in representation theory (for obvious reasons) and in physics, particularly in encoding symmetries of quantum systems. But it is just one in a family of higher enveloping algebras: each dg Lie algebra g has an enveloping E_n algebra U_n(g). (Here E_n refers to "n-dimensional algebras" in the sense of the little n-disks operad.) This construction admits a nice presentation via factorization algebras, by work of Knudsen, and we will discuss how it relates to symmetries of quantum field theories. We will discuss a model for the *center* of U_n(g) and how this framework encodes the observables of a bulk-boundary system where the bulk is topological BF theory for Lie algebra g and the boundary encodes "topological currents." (This is joint work with Greg Ginot, Brian Williams, and Mahmoud Zeinalian.)

Talk slides: Centers of higher enveloping algebras and bulk-boundary systems