Timeline for Bar notation in Bourbaki’s *Lie groups*, Chap. IX
Current License: CC BY-SA 4.0
10 events
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| Feb 3, 2020 at 6:59 | comment | added | abx | @Francois Ziegler: Oops, you are right, I was too hasty. Of course this is the same vector space, but viewed inside $\mathfrak{g}_{\mathbb{C}}$. | |
| Feb 3, 2020 at 6:02 | comment | added | Francois Ziegler | @abx Is it? That Appendix would seem to define $\overline{\mathfrak p}$ as “$\mathfrak p$ where $\alpha\in\mathbf C$ now acts by $v\mapsto\overline\alpha v$”, whereas the exercise talks about $\mathfrak p+\overline{\mathfrak p}$ and $\mathfrak p\cap\overline{\mathfrak p}$. | |
| Feb 3, 2020 at 5:35 | comment | added | abx | It is clearly explained in Appendix II of the chapter. Indeed one may argue that a reference to that appendix would have been appropriate — though at this stage it is likely that the reader won't have any doubt about the meaning of that notation. | |
| Feb 2, 2020 at 23:59 | comment | added | LSpice | The notion of conjugation with respect to a real form is introduced on p. 16. Searching for 'conjugaison' gives several results, most of the form (translated) "let $\sigma$ be the conjugation" or "let $\tau$ be the conjugation" (and then references to conjugacy classes). I can't figure out how to search for overbars, but all occurrences near the word 'conjugaison' seem to apply, properly, to complex numbers. I think that the answer is probably that it comes out of nowhere, or at least nowhere in Chapter IX. | |
| Feb 2, 2020 at 23:29 | comment | added | Francois Ziegler | Neither could I! (Further re-tagged in agreement with your comment.) | |
| Feb 2, 2020 at 23:26 | history | edited | Francois Ziegler |
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| Feb 2, 2020 at 23:22 | comment | added | YCor | Your question seems to be specifically about Bourbaki (namely the treatise), so I added the tag. The notation has nothing to do with Lie algebras, since it makes sense in the complexification of an arbitrary real vector space. Given Bourbaki's principles it's certainly introduced somewhere, and I would have guessed somewhere in the Algebra books, but can't locate it there. | |
| Feb 2, 2020 at 23:13 | history | edited | YCor |
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| Feb 2, 2020 at 20:32 | history | edited | Francois Ziegler | CC BY-SA 4.0 |
Link French original too
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| Feb 2, 2020 at 20:27 | history | asked | Francois Ziegler | CC BY-SA 4.0 |