Quantum group notation I was jumping into the deep end and reading a few papers and lectures on quantum groups. My knowledge on Lie algebras is a bit thin but I was just wondering the notation used in the starting of this document:

One should have $U_\hbar(g) = U(g)[[\hbar]]$ as a vector space [...]

My question is, is the $\hbar$ the Cartan subalgebra $\mathfrak{h}$ I have been seeing in other papers, and what does the $U(g)[[\hbar]]$ mean precisely? Usually I see the quantum group notated as $U_q(g)$, so the sudden change in notation concerned me. Thanks in advance!

Usually $\hbar$ is simply the reduced Planck constant $h/(2\pi)$.
I have sadly no idea why it is featured such prominently in your context.
