TITLE: Fraktur symbols for Lie algebras
QUESTION [32 upvotes]: Does anyone know when and why the Fraktur script was introduced for Lie and other algebras—$\mathfrak{g}$, $\mathfrak{gl}_n$, $X/\mathfrak{g}$,
$\mathfrak{g}\oplus\mathfrak{g}$, $\mathfrak{su}$, $\mathfrak{M}_g$, etc.?
And introduced by whom?
Is its use pretty much restricted to algebra, or was it in the past employed in, say, geometry as well, but has only survived to the current time within algebra?
(Or maybe it is currently used outside of algebra and I am just ignorant of those areas.)
The typeface itself goes back to the 15th century.
The generally illuminating website "Earliest Uses of Various Mathematical Symbols" seems not to shed light on this issue.
I find the Fraktur font adds a certain elegance and mystery to the subjects that utilize it!
I'm a bit envious, not working in those fields... —$\mathfrak{Joseph}$ :-)

REPLY [3 votes]: Let me point out a counter-example, in which Fraktur is not used for Lie-algebras.
It's Непрерывные группы (literally "Continuous Groups") by Lev Pontryagin, published in 1946 in the USSR. (Sorry, in fact, I have a Japanese translation from the second Russian edition in 1954. It is "連続群論" in 1957. See Worldcat entry for the bibliography.) It uses Fraktur for classical Lie groups(!), and Roman for their Lie algebras.
See the middle of p. 521, the left photo. The word "リー群" means "Lie group(s)", as you can see from the Japanese Wikipedia page. At the bottom of the same page, it says "$\mathfrak{H}_r$ のリー代数 $H_r$" ($\mathfrak{H}_r$'s Lie algebra $H_r$). See also p. 545, the right photo. You can see the Dynkin diagrams of the classical and exceptional Lie algebras.
    

Click to enlarge. These photo citations must be ok under the copyright law.
(I originally posted this as a MSE question. I think these photo citations are allowed under the copyright )