Timeline for Direct sum of representations of a compact quantum group
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4, 2020 at 17:55 | comment | added | user167952 | You can probably help with this, if you are interested and have some spare time: mathoverflow.net/questions/378143/… Thanks in any case! | |
| Dec 2, 2020 at 15:29 | comment | added | user167952 | I think I understand now! Thanks again :) | |
| Dec 2, 2020 at 15:16 | comment | added | Matthew Daws | I'm not using that; I'm proving that...! In the penultimate paragraph, I use that this relation holds on $\mathcal B_0(H) \otimes A$. This is obvious. That is extends to the multiplier algebra is not obvious, and that's what my (sketchy) argument proves. | |
| Dec 2, 2020 at 13:59 | comment | added | user167952 | I had a detailed look at your answer and I think you are just sweeping the technical parts under the identification carpet. It still looks like you are implicitely using something like $(id_H \otimes \Delta)(\tau_\alpha v_\alpha) = \tau_\alpha(id_{H_\alpha} \otimes \Delta)(v_\alpha)$ where $\tau_\alpha$ is the inclusion map $B(H_\alpha \otimes K) \to B(H \otimes K)$ on the left and similarly $\tau_\alpha: B(H_\alpha \otimes K \otimes K) \to B(H \otimes K \otimes K)$ on the right. This was exactly my question, so maybe I am just misunderstanding your answer. | |
| Dec 2, 2020 at 12:50 | comment | added | user167952 | Was just a little bit of unsure :) Thanks for the confirmation! | |
| Dec 2, 2020 at 12:38 | comment | added | Matthew Daws | Erm, yes! Not sure what else to say. | |
| Dec 2, 2020 at 12:08 | comment | added | user167952 | Thanks! One more question: don't we actually need that $\sup_i \| v_i\| < \infty$ to define the direct sum? Otherwise $\bigoplus v_i$ won't be a bounded operator I think. Of course, in practise the representations are unitary and then this is no problem? | |
| Dec 1, 2020 at 14:03 | vote | accept | CommunityBot | ||
| Nov 30, 2020 at 15:47 | history | answered | Matthew Daws | CC BY-SA 4.0 |