Timeline for Duality between orbifold and quasi-Hopf algebra (twisted quantum doubles)
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10 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jan 10, 2014 at 5:13 | comment | added | wonderich | @ Matthew, thanks, please feel free update as an answer if you also have some inputs. I need to do some extra work or you may rephrase it to help digesting it. | |
| Jan 2, 2014 at 4:39 | comment | added | Matthew Titsworth | The reason that I ask is that below, Marcel uses Muger's result to provide a $G$-orbifold CFT whose representation category is the representation category of $D^\omega(G)$. However, the statement from which you draw your inital observation goes no further than saying that the two are Grothendieck equivalent. | |
| Jan 2, 2014 at 4:22 | comment | added | Matthew Titsworth | What it seems like you mean by duality is that the representation categories of $D^\omega(\mathbb H_8)$ for some $\omega$ and $SU(2)/(\mathbb Z_2 \times \mathbb Z_2)$ are described by the same fusion ring. To clarify then, it seems like what you are asking is this: Given $G,H$ finite groups and $\omega\in H^3(H,U(1))$, is there a G-orbifold theory with fusion ring isomorphic to the fusion ring for $D^\omega (H)$ and if so, what is there relationship? | |
| Jan 1, 2014 at 2:36 | answer | added | Marcel Bischoff | timeline score: 2 | |
| Dec 31, 2013 at 22:56 | comment | added | wonderich | See also this post Phy.SE on orbifolds of SU(2)/G' and SO(3)/G' if there are available data in the literature, please let me know. Many thanks! | |
| Dec 31, 2013 at 22:54 | comment | added | wonderich | But are there some known examples appear between the twos? e.g. In my post I had provided one example. Examples are fine, it needs not to be very general. Physicists appreciate (many) examples more than a theorem. :) | |
| Dec 31, 2013 at 22:50 | comment | added | S. Carnahan♦ | The question of finding orbifold constructions of fusion rings is very natural and interesting. On the other hand, I don't see much evidence of a general duality here, since the rings are relatively small. | |
| Dec 31, 2013 at 22:28 | history | asked | wonderich | CC BY-SA 3.0 |