TITLE: Introduction to W-Algebras/Why W-algebras?
QUESTION [22 upvotes]: Does anyone know of an introduction and motivation for W-algebras?
Edit: Okay, sorry I try to add some more background. W algebras occur, for example when you study nilpotent orbits: Take a nice algebraic/Lie group. It acts on its Lie-algebra by the adjoint action. Fix a nilpotent element e and make a sl_2 triple out of it. A W algebra is some modification of the universal enveloping, based on this data.
A precise definition is for example given here: https://arxiv.org/pdf/0707.3108.
But this definition looks quite complicated and not very natural to me. I don't see what's going on. Therefor I wonder if there exists an easier introduction.

REPLY [2 votes]: The motivation did not change. The theory of finite W-algebras advanced quite a bit, imho, mostly thanks to the works of Losev.
There is a good introductory text by Arakawa now.