Timeline for In which commutative algebras does any derivation possess a flow?
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
|
|
| Oct 21, 2013 at 17:56 | answer | added | Qiaochu Yuan | timeline score: 3 | |
| Sep 27, 2010 at 16:59 | vote | accept | Fiktor | ||
| Sep 24, 2010 at 12:59 | answer | added | Tom Goodwillie | timeline score: 3 | |
| Sep 24, 2010 at 2:18 | comment | added | Tom Goodwillie | But surely the usual flow associated to a smooth tangent vector field on a smooth closed manifold does not satisfy the condition written down in the question for an <i>arbitrary</i> $\mathbb R$-linear map $h:A\to\mathbb R$. | |
| Sep 24, 2010 at 2:03 | comment | added | Tom Goodwillie | Formal power series rings? Rings of analytic functions? | |
| Sep 23, 2010 at 23:07 | history | edited | Fiktor | CC BY-SA 2.5 |
Adding an example
|
| Sep 23, 2010 at 19:09 | comment | added | Yemon Choi | I may have misunderstood your question; but if I recall correctly there are commutative algebras A which admit no non-zero derivation from A to A -- in fact every semisimple Banach algebra has this property, this is Marc Thomas' improvement on the Singer-Wermer theorem. (Note that I'm not assuming the derivation is continuous.) I suspect that if A has no non-zero derivations, then every derivation will be a flow -- but this is somehow not the kind of example you are looking for... | |
| Sep 23, 2010 at 17:33 | history | edited | Fiktor | CC BY-SA 2.5 |
typo
|
| Sep 23, 2010 at 17:27 | comment | added | Fiktor | @Theo Johnson-Freyd Yes, "non-compact". Corrected. Thank you. | |
| Sep 23, 2010 at 17:26 | history | edited | Fiktor | CC BY-SA 2.5 |
typo
|
| Sep 23, 2010 at 16:32 | comment | added | Theo Johnson-Freyd | There is some typo in "1'. Algebra $C^\infty(M)$ of smooth functions on a compact manifold without boundary". Presumably you mean "non-compact"? In any case, nice question overall. | |
| Sep 23, 2010 at 14:09 | answer | added | Greg Muller | timeline score: 4 | |
| Sep 23, 2010 at 13:21 | history | asked | Fiktor | CC BY-SA 2.5 |