Timeline for Eigenvalues of the free sphere
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 8, 2013 at 12:59 | vote | accept | Richard | ||
| Jan 8, 2013 at 11:29 | answer | added | Uwe Franz | timeline score: 10 | |
| Jan 8, 2013 at 1:59 | comment | added | Branimir Ćaćić | @Z254R Is $\sqrt{d^\ast d}$ actually going to give you the "Dirac operator" of a spectral triple? From the look of it, I'd sooner expect $\sqrt{d^\ast d}$ to only be the absolute value of such an operator, and finding the correct "sign" is often the tricky part with constructing spectral triples from the ground up. | |
| Jan 6, 2013 at 22:19 | comment | added | Alexander Chervov | Algebraic approach has advatage that it works on non-compact situations, so I would be very interested to know what can be "Casimir" for "free-R^n" - it should be related to our Manin matrices, but I do not see how this can be approached for the moment... | |
| Jan 6, 2013 at 22:14 | comment | added | Alexander Chervov | Actually I do not see correct analogs of "Casimirs" in free setup... that is why it is somewhat surprising for me what you write... I may be quite wrong... Just feelings... | |
| Jan 6, 2013 at 20:40 | comment | added | Alexander Chervov | for usual sphere we can do everything with algebra and NO analysis - sl(n) will act on sphere and Laplacian (=dd^*) = Casimir (center of U(sl)), and hence representation theory of sl(n) applies. Do expect something like this for "free-sphere" ? At least do you expect that non-commutative polynoms of degree less than "k" will be preserved by hypothetical Laplacian dd^* ? | |
| Jan 6, 2013 at 15:22 | comment | added | Liviu Nicolaescu | Also, the metric enters in a more subtle way in the definition of $d^*$. The notion of adjoint uses some metric. | |
| Jan 6, 2013 at 14:53 | comment | added | Alexander Chervov | please read second sentence as: At the moment it is not clear for me how to define "d" IN "free" setup ? | |
| Jan 6, 2013 at 14:51 | comment | added | Alexander Chervov | I would add emphasize that main difference on "free-Sphere" from "just Sphere" is that x_i do NOT COMMUTE (just emphasize for better reading). At the moment it is not clear for me how to define "d" is "free" setup ? And also not clear for me definition of $\perp$, both free and non-free. Can we define "d" for "free-space" I mean if we do not impose condition $\sum x_i^2 =1 $ ? What will be the answer in this case ? | |
| Jan 6, 2013 at 14:29 | history | asked | Richard | CC BY-SA 3.0 |