Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Does anyone know how it has become the standard to express Lie algebras in fraktur? I'd also like to know how it's established for each era and region, not only the origin.

It doesn't seem that Pontrjagin's book, "Topological Groups", published in USSR in 1946 and the second revision in 1954, used fraktur. (It's a mere guess, judging from the Japanese translation which didn't employ fraktur. FYI, it uses Fraktur for Classical Lie groups(!), and their Lie algebras in Roman.)

The wikipedia page on Lie algebra didn't mention at all that they're in fraktur, so I wrote it just now. Thanks beforehand.

EDIT: The original quetion didn't say "I'd also like to know how it's established for each era and region, not only the origin.", and I added it after the first answer.

share|improve this question
See mathoverflow.net/questions/87627/… –  Cocopuffs Sep 17 '12 at 13:50
Thanks! First I wondered how I failed to search, but it's in mathoverflow. ;-) –  teika kazura Sep 18 '12 at 8:43
add comment

1 Answer

To reiterate what is said in the MO post (thanks Cocopuffs), Lie theory was birthed (mostly) in Germany. Sophus Lie worked closely with Felix Klein for a quite a long time. Lie's student Friedrich Engel was German. Wilhelm Killing was German. So the early fathers of Lie theory were pretty much all German (or working in Germany).

That seems to be why Fraktur letters are used for Lie algebras.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.