Timeline for algebra-geometry duality
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4, 2013 at 18:15 | comment | added | Qiaochu Yuan | @Francois: you can get complex-valued functions (as a C*-algebra) by tensoring real-valued functions with $\mathbb{C}$ and remembering the action of complex conjugation. They're equivalent data. | |
| Dec 4, 2013 at 16:44 | answer | added | Joseph Van Name | timeline score: 3 | |
| Dec 4, 2013 at 16:39 | comment | added | abx | This is certainly true if $S$ and $T$ are compact Hausdorff, since then $S$ can be identified with the set of maximal ideals of $\mathcal{C}(S,\mathbb{R})$ endowed with the Zariski topology. | |
| Dec 4, 2013 at 16:33 | comment | added | Francois Ziegler | Can you confirm that you insist on real-valued functions only? Well-known theorems of the kind you require (such as Gelfand-Naimark for compact spaces) use complex-valued functions instead. | |
| Dec 4, 2013 at 16:18 | review | First posts | |||
| Dec 4, 2013 at 16:31 | |||||
| Dec 4, 2013 at 16:16 | comment | added | Neil Epstein | Well, I guess it works if you assume $S$ and $T$ are discrete. On the other hand, if you don't assume Hausdorff (or, probably, $T_3$), I imagine it can't work. | |
| Dec 4, 2013 at 15:59 | history | asked | clark | CC BY-SA 3.0 |