Timeline for Does every locally compact, simply connected group admit enough finite dimensional representations?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2022 at 20:22 | vote | accept | Rick Sternbach | ||
| Jan 16, 2022 at 17:18 | comment | added | Onur Oktay | Please see the article ams.org/journals/tran/1980-259-02/S0002-9947-1980-0567087-9 | |
| Jan 16, 2022 at 15:46 | answer | added | Daniel Beltita | timeline score: 4 | |
| Dec 12, 2021 at 11:04 | comment | added | YCor | The smallest counterexample is the universal covering of $\mathrm{SL}_2(\mathbf{R})$, which is even contractible (homeomorphic to $\mathbf{R}^3$). Possibly it is easier to prove non-linearity (without continuity) for the 2-fold covering of $\mathrm{SL}_n(\mathbf{R})$ for larger $n$. These contain f.g. non-residually-finite subgroups, but I'd like an elementary argument for this. | |
| Dec 12, 2021 at 8:33 | comment | added | Uri Bader | Ben Wieland answered this in the negative in a comment to the original question, assuming continuity. This assumption is not needed really, by the work of Borel-Tits on "abstract homomorphisms". | |
| Dec 12, 2021 at 5:01 | history | asked | Rick Sternbach | CC BY-SA 4.0 |