Timeline for What are the important open problems about Lie groups?
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6 events
| when toggle format | what | by | license | comment | |
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| Aug 24, 2023 at 16:53 | comment | added | Denis T | @SamHopkins I was about to write this as well, but after a second thought I'd say that Smith conjecture is not really about Lie groups; similarly to 5th Hilbert problem, Gleason theorem, Hofmann-Morris theorem and such, it's about unexpected niceness of fluid and wild general topological groups, rather than some immanent (...maybe it is better to say "natural and intrinsically definable") properties of very algebraic, very rigid Lie groups. | |
| Aug 24, 2023 at 15:25 | comment | added | Sam Hopkins | I think the Hilbert--Smith conjecture is a very famous and old problem about Lie groups: en.wikipedia.org/wiki/Hilbert%E2%80%93Smith_conjecture | |
| Aug 24, 2023 at 15:19 | comment | added | Denis T | And another folklore one, which is probably not very important, but very much open and intriguing. Do simple discrete subgroups of Lie groups exist? Here's a good summary of current progress mathoverflow.net/q/90058/81055 | |
| Aug 24, 2023 at 15:04 | comment | added | Denis T | In addition to my answer, I know that there are (potentially) much more accessible conjectures in area of approximation theory: which groups are hyperlinear? how different pseudoinvariant metrics on Lie groups behave under homomorphisms? (I'd suggest to look at talks/papers by A. Lubotzky for context and precise statements). Also there are some problems regarding images of word maps and their action on Haar measure, connected to (pro)finite group theory; for me this is mostly hearsay, so I hope that somebody can elaborate on those topics. | |
| Aug 24, 2023 at 14:49 | answer | added | Denis T | timeline score: 11 | |
| Aug 23, 2023 at 6:35 | history | asked | cgb5436 | CC BY-SA 4.0 |