Category , lie algebras ....

Question

I want a reference book about Lie algebras that have the definition of universal enveloping algebra by the categorical point of view. All references that i found use the construction by the quotient of the tensor algebra and one especific ideal.

Answer 1

An internet-accessible note that emphasizes a bit more the characterization, rather than construction, is in my course notes, http://www.math.umn.edu/~garrett/m/mfms/notes_2013-14/11d_diffops.pdf

In my experience, orthodox texts don't so much emphasize this viewpoint, because they're (misguidedly, in my opinion) trying to be "elementary", and, given the standard curriculum, even the mildest most innocent categorical notions are viewed with suspicion, as though they were an additional burden rather than useful.

Serre's 1964 (?) Harvard notes, published by Benjamin long ago, form an orthodox source more progressive in this regard than many since.