What does the notation $U\mathfrak{sl}_2$ mean, and why is the $U$ written in a different typeface to the $\mathfrak{sl}$?

Question

A representation theory homework problem asks me to determine the finite dimensional irreducible representations and the finite dimensional indecomposable representations of $U\mathfrak{sl}_2$. I suppose this is standard notation, but I'm not sure what is meant by it.

Question. What does the notation $U\mathfrak{sl}_2$ mean, and why is the $U$ written in a different typeface to the $\mathfrak{sl}$?

What's the general pattern here, and how do you puzzle these things out yourself?

Answer 1

This probably means the universal enveloping algebra, though it is unusual to see it written without brackets (I would usually expect it to be written as $U(\mathfrak{sl}_2)$).