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As far as I understand, each chapter of the Bourbaki's collection was written by one (or two?) specific authors. The book itself was reviewed, corrected and after all approved by the whole Bourbaki assembly (if I may call them this way). But I have the feeling one (or two) specific person was in charge of the writting of any given chapter.

In my opinion, the style and the clarity of the exposition really varies from one book to the other. I personally found the Lie Algebras book much more readable than the Algebra one. I haven't read any other volume of the Bourbaki's series, so I don't have an opinion on the other chapters. In any case, I'd like to know if one has any idea (or convictions) on the identity of the authors of each volume. Let me start filling the boxes where I am almost convinced I am correct:

$\bullet$ Algebra (at least chapter 4 to 7?) : Adrien Douady (may be wrong as he is said to have joined after the beginning of the writting of Algebra 4-7)?

$\bullet$ Espaces vectoriels topologiques (the whole book?) : Alexandre Grothendieck.

Possible guess following suggestions in the comments:

$\bullet$ Lie Algebras : François Bruhat (in connection with his co-author Jacques Tits)?

$\bullet$ Functions of a real variable : Jean Delsartes?

Any guess for the other chapters/books?

EDIT : Following @abx remark (who actually was one of the later Bourbaki's member, so he can be trusted on that point), one should rather ask for the author of the preliminary draft of each chapter. This, in any case, is what I was looking for. I am definitely not interested in the various identities of the members who polished the initial version of the draft.

EDIT BIS : Matthieu Latapy suggests a very interesting approach using comparison of n-gram distributions between the Bourbaki's chapters and some contemporary papers of the suspected authors. I must confess I don't have any idea on how to implement that effectively. But I'd very interested to know if it can be used to match François Bruhat with some chapters in Lie-Algebras, Adrien Douady with some chapters in Algebra and Commutative Algebra with Samuel/Chevalley/Cartier.

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    $\begingroup$ My understanding is that Tits wrote most of the Lie theory books. $\endgroup$
    – Irina
    Mar 23, 2021 at 21:32
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    $\begingroup$ Wouldn't it make sense to compare the word or n-gram frequency distributions in these texts to the ones in contemporary texts with known authors, suspected to hide behind Bourbaki? One may even use modern machine learning approaches to the problem: towardsdatascience.com/… $\endgroup$ Mar 23, 2021 at 22:13
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    $\begingroup$ @Libli According to Linus Kramer, Chapters IV, V, and VI of Groupes et Algèbres de Lie was "heavily influenced" by Tits. Siobhan Roberts corroborates this claim. But of course that doesn't prove that Tits actually wrote those chapters. Wikipedia claims that it was Armand Borel who pushed for the inclusion of illustrations (unusual for Bourbaki) in Chapters IV, V, and VI. $\endgroup$ Mar 24, 2021 at 4:22
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    $\begingroup$ More generally, it is known that Jean Dieudonné was one of the most prolific members of Bourbaki when it came to actual writing. $\endgroup$ Mar 24, 2021 at 4:34
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    $\begingroup$ At the Bourbaki archives you can find lots of information about authors writing certain "rédactions", albeit only up to 1954. They show in particular that some of the OPs claims are not true. $\endgroup$ Mar 24, 2021 at 5:49

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I think the whole idea is wrong. As you can see from the Bourbaki archives, Bourbaki worked as follows: one member would write a rough first draft, this would be read in the next meeting, criticized, heavily modified, then another member would write a new version, and so on. It is impossible to attribute any of the books to one author. By the way, all guesses in the post or in the comments are wrong: Algebra 4-7 was started much before Douady joined Bourbaki, Tits was never a member, etc.

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    $\begingroup$ @abs : Thanks for the info. As many chapters of the book "Algèbres et théories Galoisiennes" by Douady and Douady are litterally copy-pasted from Chapters 4 to 7 of Algebra (with the same litle mistakes in the understanding of the relations between étale and diagonal algebras), I had assumed the authors took this liberty because one of them actually wrote part of Algebra 4 to 7. You seem to imply that my interpretation is incorrect. Following your suggestion, I will edit my question. $\endgroup$
    – Libli
    Mar 24, 2021 at 9:00
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    $\begingroup$ It could very well be that Douady wrote one of the last versions. But on the Bourbaki archive site there are versions dating from 1947, when Douady was 12... $\endgroup$
    – abx
    Mar 24, 2021 at 11:26
  • $\begingroup$ @Libli: I just came across this thread and your remark. Could you elaborate on what you meant by "the same little mistakes in the understanding of the relations between etale and diagonal algebras"? Examples of such mistakes? Where can I find corrections? Thanks! $\endgroup$
    – W Sao
    Apr 25 at 20:32
  • $\begingroup$ @WSao : I don't remember precisely, though they were mostly of typographic type. I remember also one stated equivalence happened to be only an implication, but that was pretty obvious. As far as edits are concerned, i am not sure they have been ever written... $\endgroup$
    – Libli
    Apr 27 at 15:39

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