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A while ago, a colleague told me that he thought he remembered that there were typos in Bourbaki's tables in the English translation of "Groupes et algèbres de Lie", but that he could no longer find his notes indicating the specific typos. Since I rely heavily on Bourbaki's tables when doing case-by-case classifications, I get very nervous at the thought that I might be using wrong tables.

Are you aware of any such typos, especially in Plates I–IX at the end of the book, in either the English or the French version?

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    $\begingroup$ I don't know about Bourbaki. Springer’s table of indices [25], T. A. Springer, Linear algebraic groups, second ed., Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2009., pp. 320-321, has an error in one form of E7, corrected in my dynkin-diagrams package. $\endgroup$
    – Ben McKay
    Commented Sep 5, 2022 at 13:52
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    $\begingroup$ My LaTeX package ctan.org/pkg/dynkin-diagrams. Springer's 14th entry is not correct, and the correction is to fill in the rightmost hollow circle. I found that out on Mathoverflow somewhere. See page 28 in the documentation of my package. $\endgroup$
    – Ben McKay
    Commented Sep 6, 2022 at 9:52
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    $\begingroup$ See mathoverflow.net/questions/243389/… $\endgroup$
    – Ben McKay
    Commented Sep 6, 2022 at 10:25
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    $\begingroup$ The French 2007 Springer edition still has the mistakes from the 1981 edition, it seems, together with the corresponding errata table mathoverflow.net/questions/429790/… $\endgroup$
    – David Roberts ♦
    Commented Feb 7, 2023 at 1:19
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    $\begingroup$ This is why it's called "Lie". :-) (in case you don't understand I made a joke). $\endgroup$
    – Alan
    Commented Feb 8, 2023 at 15:14

2 Answers 2

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Not speaking to the English edition, but:

I have (an electronic version of) the 1981 Masson edition (in French) of books IV-VI of the LIE volume, and that one contains a list of typos at the end. You seem to be interested in the root system tables which, I guess, would be the "Planches" on p. 250-275 in that edition; it's sometimes a good idea to cross-check those with sections 5-14 of book VI par. 4 no. 4 where those results are derived, which in that edition are on page 202-222. In that case, the last page of typos is all you need:

enter image description here

Basically the only important one is the one on p. 256, which gives an incorrect description of some positive roots, in terms of the common basis, in type $D_\ell$. (The next typo, for page 257, is extremely pedantic: For all I know, the equality signs $=$ there should just be isomorphism $\simeq$ signs ...)

If anyone knows of more typos in that edition, not caught in the list above, I'd be happy to know.

Of course, other editions, in particular English ones, might have more typos. I do remember coming across some instances in the exercises about buildings (that is, to book IV paragraphs 1 and 2), where the English translation I had introduced errors absent from the original, and used differing translations for the same original French terminology. But I have lost my notes for those.

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    $\begingroup$ Page 197 of the 2007 Springer version (ch VI \S 4.2, Théorème 3) still has the mistake for $E_6$ noted in the above table (it's missing the downward-pointing edge and bottom node on the Dynkin diagram). Similarly for the error in the Type $D_l$ table on page 256. The errata table is included verbatim, it seems. $\endgroup$
    – David Roberts ♦
    Commented Feb 7, 2023 at 1:18
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    $\begingroup$ This is already very helpful, and actually the electronic edition I have, hence the one I reference most often, is the French one. Thank you! Given the age of this question I suspect that there's no collective rush to answer about the English edition, but, just in case, I'll give it a day or two more before accepting. $\endgroup$
    – LSpice
    Commented Feb 7, 2023 at 17:56
  • $\begingroup$ Re, a day or two, or two months, it seems. Whoops! $\endgroup$
    – LSpice
    Commented Apr 13, 2023 at 16:44
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There is a typo that I found last year: on page 216 "Système de type $E_{7}$", the second fundamental weight $\varpi_{2}$ should be $$\frac{1}{2}(4\alpha_{1}+7\alpha_{2}+8\alpha_{3}+12\alpha_{4}+9\alpha_{5}+6\alpha_{6}+3\alpha_{7})$$ instead of $\cdots +8\alpha_{6}+\cdots$.

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    $\begingroup$ Great; thanks! This one is correct in Planche VI at the back (p. 265), so I'd never noticed. $\endgroup$
    – LSpice
    Commented Feb 8, 2023 at 15:27

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