User talk:Francesco Cattafi

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The Strauss Dynasty moved to draftspace

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Harish-Chandra's proof of Lie's third theorem

Hi,

About your recent addition of remarks on proofs of Lie's third theorem (which are very nice). If I remember correct, I heard that there was a proof of the theorem by Harish-Chandra. Do you know anything about it? Is it one of the three mentioned in the article? (I did a quick Google search but couldn't find anything so maybe my memory was wrong.) Taku (talk) 08:16, 19 September 2022 (UTC)[reply]

Hi, thanks for the question! Unfortunately I have never heard about such proof, but after a bit of searching online I found these notes, https://math.mit.edu/~ngtriant/notes/ados_theorem.pdf, where they mention that Harish-Chandra actually provided in 1949 a proof not of Lie's third theorem but of Ado's theorem. Indeed, I just read now that in the page Ado's theorem they mention his paper among the references. Unfortunately they don't mention anything else about the actual proof(s) of the result, and I have actually never read it myself so I wouldn't be able to improve that article (but it would be nice if someone else could!) Francesco Cattafi (talk) 16:36, 25 September 2022 (UTC)[reply]

First my apology for the late response. Second, thank you for doing some digging in history. After reading your response, I do now think I misremember; it was Ado's history not Lie's third theorem (though, of course, they are closely related). In any case, the right place to mention Harish-Chandra's proof is therefore at the Ado's theorem article. If I can find time, I will try to read Harish-Chandra's proof and see if it differs from the standard one (and edit the article accordingly). Anyway thank you again for the response. -- Taku (talk) 09:00, 18 November 2022 (UTC)[reply]

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Colloquium Lectures (AMS) moved to draftspace

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Proposed deletion of Momo (TV series)

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Lie algebroid

Hi,

It appears that you wrote most of the article on Lie algebroids, and so perhaps you could answer a question on the talk page there. Very early in the article, it says the anchor is a derivation (Liebnitz rule) and it uses a dot product to define what this is. Based on context, it looks like some bundle metric, but I can't guess what this is, and why it is not an explicit part of the definition. (Surely, if one is going to be taking vector products, this should be an explicit part of the definition, right?) Now, this particular text predates your additions, but I figure you'd be able to answer it easily. Thanks. 67.198.37.16 (talk) 21:05, 29 May 2024 (UTC)[reply]

Never mind. I just realized the whole thing is a scalar, so this is a scalar product, not vector. Dohh. I'll edit the article to clarify this per talk page. Please review for correctness. 67.198.37.16 (talk) 21:21, 29 May 2024 (UTC)[reply]

Thanks again for the message and sorry for my late reply - I have reviewed your edit and replied in the talk page! Francesco Cattafi (talk) 13:44, 29 June 2024 (UTC)[reply]