Timeline for $p$-adic exponentials for $p$-adic Lie groups
Current License: CC BY-SA 3.0
7 events
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| Dec 3, 2017 at 18:59 | comment | added | Jim Humphreys | @nfdc23: The 1964 Harvard lectures Lie Algebras and Lie Groups by Serre (published in typewritten large format by W.A. Benjamin in 1965, with some symbols added by hand) are as you say another useful reference. This is close to the formal treatment in Bourbaki's treatise, Chap. 1-3. (Apparently Serre himself had a major role in developing the Bourbaki approach.) | |
| Dec 3, 2017 at 18:48 | comment | added | Jim Humphreys | @YCor: I was only referring to the narrower question about exponentiation raised by the paper I was linking to. Naturally there are many roles for $p$-adic Lie groups and their Lie algebras. | |
| Dec 2, 2017 at 23:11 | comment | added | YCor | I'm not sure what is meant by "it's not easy to say much about the use of exponentials in $p$-adic Lie groups". Typically there are many problems about general totally disconnected locally compact groups for which the case of $p$-adic Lie groups is a natural easy test-case, precisely because of the use of the Lie algebra. And it's not only useful for compact $p$-adic Lie groups. For instance, the classification of topologically simple non-discrete $p$-adic Lie groups is easy to carry out using the Lie algebras. | |
| Dec 2, 2017 at 22:40 | comment | added | M.G. | Schneider has a book on p-adic Lie groups that grew out of his lectures. P-adic analytic groups are also treated in Dixon-Sautoy-Segal's "Analytic Pro-p-Groups" book. Both treat the exponential map and much more. | |
| Dec 2, 2017 at 20:47 | comment | added | nfdc23 | Serre's book called something like "Lie algebras and Lie groups" also has a self-contained discussion of this stuff (including applications to versions of Lie's three theorems), so that could be another reference (maybe not "explicit literature", whatever that may mean?). | |
| S Dec 2, 2017 at 20:10 | history | answered | Jim Humphreys | CC BY-SA 3.0 | |
| S Dec 2, 2017 at 20:10 | history | made wiki | Post Made Community Wiki by Jim Humphreys |