Timeline for Is every group the automorphism group of a ring?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Aug 3 at 4:29 | comment | added | Qiaochu Yuan | @Ewrt: this is incredible overkill, there is no need to discuss either $\ell^2$ or bounded operators here. Every group $G$ already acts by automorphisms on, say, the polynomial ring in $|G|$ generators, by permuting the generators. | |
| Feb 1 at 22:09 | answer | added | Brian Pinsky | timeline score: 9 | |
| May 3, 2023 at 12:50 | comment | converted from answer | Ewrt Wert | (Comment: If you accept subgroup of automorphism groups, then it's easy: Every group can be represented on the ring $B(\ell^2(G))$ by left regular representation $g \mapsto U_g$ and is so subgroup of $Aut(B(\ell^2(G)))$ by inner automorphisms induced by $U_g$.) | |
| May 3, 2023 at 7:47 | vote | accept | A. Bailleul | ||
| May 3, 2023 at 7:46 | history | edited | A. Bailleul | CC BY-SA 4.0 |
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| May 3, 2023 at 7:39 | comment | added | A. Bailleul | @YCor I am mostly interested in the associative unital case. | |
| May 3, 2023 at 3:26 | history | became hot network question | |||
| May 2, 2023 at 20:03 | answer | added | M.G. | timeline score: 14 | |
| May 2, 2023 at 19:48 | history | edited | YCor |
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| May 2, 2023 at 19:48 | comment | added | YCor | Could you define exactly what you mean by ring, since there are many definitions according to different communities. (Unital? Associative? Commutative?) | |
| May 2, 2023 at 19:48 | comment | added | Dave Benson | Ah, true. But some construction based on the graph should work... | |
| May 2, 2023 at 19:47 | history | edited | YCor |
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| May 2, 2023 at 19:46 | comment | added | Wojowu | @DaveBenson I believe that ring will usually have many more automorphisms than those of the graph it comes from. | |
| May 2, 2023 at 19:44 | comment | added | Dave Benson | Since every group is the automorphism group of a graph (even a cubic graph), can't you just use the Stanley-Reisner ring of the graph over a field of your choice? | |
| May 2, 2023 at 19:24 | history | asked | A. Bailleul | CC BY-SA 4.0 |