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Does anyone know who was the first to coin the term "Lie group"?

The following thesis from 1928 suggests that the term was already in use by that time: "Systems of Two Differential Equations from the Lie-Group Standpoint"

(http://genealogy.math.ndsu.nodak.edu/id.php?id=6129)

I've also found the term in the book "Theory of functionals and of integral and integro-differential equations" by Vito Volterra from 1930.

Does anyone have any idea when the term was first used? Someone suggested that Weyl or Brauer might have been the first to use the term, but I haven't found anything.

asked Jul 4 2011 at 13:54

David Corwin

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jeff560.tripod.com/l.html says 1891. – Qiaochu Yuan Jul 4 2011 at 14:03

I would accept that as an answer, but it's a comment ;) – David Corwin Jul 4 2011 at 15:08

It seems likely that Lovett coined the term, but if anyone finds evidence to the contrary, please let me know. – David Corwin Jul 4 2011 at 15:09

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@Davidac897 Why do you say that Lovett coined the term if Qiaochu's link has a reference to a paper of Autonne using the term 6 years earlier? Another place to look is E. Cartan's thesis: books.google.com/books?id=JY8LAAAAYAAJ – Felipe Voloch Jul 4 2011 at 16:50

Willie Wong · Accepted Answer · 2011-09-11 10:30:07Z UTC

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(Just to get this off the un-answered list, I'm copying Qiaochu's comment as an answer.)

http://jeff560.tripod.com/l.html suggests it is 1891, in the paper "Sur une application des groupes de M. Lie" by L. Autonne, with first English language appearance in 1897 with an article by Lovett.

edited Sep 11 2011 at 10:30

Willie Wong

community wiki

2 revisions

	Do you/anyone know if this means Lie groups as-we-know-them-today, or rather what Serre calls group-chunks (which was, if I understand correctly, the objects Lie actually considered) – Mariano Suárez-Alvarez Sep 11 2011 at 7:26
	Lovett's article is free-view on JStor (just edited the answer to include the link). Perhaps someone more knowledgeable in the distinction can take a look at that short article and give an answer? – Willie Wong Sep 11 2011 at 10:29

When did the term “Lie group” first appear?

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