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"


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.

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    $\begingroup$ jeff560.tripod.com/l.html says 1891. $\endgroup$ Jul 4, 2011 at 14:03
  • $\begingroup$ It seems likely that Lovett coined the term, but if anyone finds evidence to the contrary, please let me know. $\endgroup$ Jul 4, 2011 at 15:09
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    $\begingroup$ @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 $\endgroup$ Jul 4, 2011 at 16:50

2 Answers 2


(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.

  • $\begingroup$ 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) $\endgroup$ Sep 11, 2011 at 7:26
  • $\begingroup$ 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? $\endgroup$ Sep 11, 2011 at 10:29
  • $\begingroup$ The term group-chunks goes back to Weil rather than Serre, I believe. $\endgroup$
    – KConrad
    May 9, 2014 at 21:33
  • $\begingroup$ Is it appropriate to edit this answer to acknowledge the earlier source pointed out by @FrancoisZiegler? $\endgroup$
    – LSpice
    Jul 27, 2019 at 17:39

Wilhelm Killing's program Zur Theorie der Lie'schen Transformations-Gruppen (Braunsberg, 1886) predates the accepted answer by 5 years. It is reprinted in his Correspondence with Friedrich Engel (1997).


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