Timeline for When does a monoidal functor between ribbon categories preserve cups and caps, but not necessarily braidings?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2014 at 15:49 | vote | accept | Manuel Bärenz | ||
| Feb 12, 2014 at 15:49 | comment | added | Manuel Bärenz | Ah, in other words, the duals only depend on the spherical element in the algebra, which can be written in terms of $q$? | |
| Feb 11, 2014 at 19:10 | comment | added | Kevin Walker | I think that one can write out bases and relations for the tensor category structure on $Rep(U_q(sl_2))$ using only powers of $q$, but that the braiding requires $q^{1/2}$. Check out Kuperberg's "spider" paper (arxiv.org/pdf/q-alg/9712003v1.pdf) and compare the tensor category relation on pages 12-14 with the braidings on page 16. | |
| Feb 11, 2014 at 18:54 | comment | added | Manuel Bärenz | When I look at the triangular element of $U_q SL(2)$ in Kassel's book, I find the $q^{1/2}$, but don't the duals depend on the triangular element as well? | |
| Feb 7, 2014 at 13:45 | comment | added | Kevin Walker | For most (all?) choices of $\xi$, the twist functor will change. | |
| Feb 7, 2014 at 8:18 | comment | added | Chris Schommer-Pries | Does this change effect the twist functor? or can that be taken to be the same in both cases? | |
| Feb 5, 2014 at 16:26 | history | answered | Kevin Walker | CC BY-SA 3.0 |