  We provide spectral Lie algebras with enveloping algebras over the operad of
little $G$-framed $n$-dimensional disks for any choice of dimension $n$ and
structure group $G$, and we describe these objects in two complementary ways.
The first description is an abstract characterization by a universal mapping
property, which witnesses the higher enveloping algebra as the value of a left
adjoint in an adjunction. The second, a generalization of the
Poincar\'{e}-Birkhoff-Witt theorem, provides a concrete formula in terms of Lie
algebra homology. Our construction pairs the theories of Koszul duality and Day
convolution in order to lift to the world of higher algebra the fundamental
combinatorics of Beilinson-Drinfeld's theory of chiral algebras. Like that
theory, ours is intimately linked to the geometry of configuration spaces and
has the study of these spaces among its applications. We use it here to show
that the stable homotopy types of configuration spaces are proper homotopy
invariants.
