Timeline for Establishing the Co-Quasi- Triangular Structure of FRT Algebras
Current License: CC BY-SA 2.5
11 events
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Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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Aug 18, 2010 at 3:05 | comment | added | Theo Johnson-Freyd | I have made some small formatting changes. | |
Aug 18, 2010 at 3:04 | history | edited | Theo Johnson-Freyd | CC BY-SA 2.5 |
small formatting changes
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Aug 17, 2010 at 21:32 | answer | added | DamienC | timeline score: 4 | |
Aug 17, 2010 at 21:25 | comment | added | DamienC | Applying the flip $\tau_{2,3}$ to $$ R_{23}R_{12}R_{13}-R_{13}R_{12}R_{23} $$ we get $$ R_{32}R_{13}R_{12}-R_{12}R_{13}R_{32} $$ which vanishes. | |
Aug 17, 2010 at 12:26 | comment | added | Abtan Massini | Ok, I agree that $ r(u^k_l \otimes I^{ij}_{mn}) = \sum_{r,s,x} R^{ji}_{rs}R^{kr}_{xn}R^{xs}_{lm} - \sum_{r,s,x} R^{ki}_{xr}R^{xj}_{ls}R^{sr}_{nm} = (R_{23}R_{12}R_{13} - R_{13}R_{12}R_{23})^{kij}_{lnm}$, but I don't see why this vanishes. In particular, I don't see why this resolves the specific problem of $R(u^2_1 \otimes I^{12}_{22})$ seeming to not equal zero.. | |
Aug 17, 2010 at 9:11 | comment | added | DamienC |
Clearly, we do have $\sum_{r,s,x} R^{ji}_{rs}R^{kr}_{xn}R^{xs}_{lm} - \sum_{r,s,x} R^{ki}_{xr}R^{xj}_{ls}R^{sr}_{nm}= (R_{23}R_{12}R_{13}-R_{13}R_{12}R_{23})^{kij}_{lnm}$ and $R_{23}R_{12}R_{13}-R_{13}R_{12}R_{23}$ is not yang-Baxter (and it does not have any meaning in terms of braids).
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Aug 17, 2010 at 3:02 | comment | added | Mariano Suárez-Álvarez | Kassel's book, if I recall correctly, has all details. | |
Aug 17, 2010 at 0:59 | history | edited | Abtan Massini | CC BY-SA 2.5 |
added 8 characters in body
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Aug 17, 2010 at 0:22 | history | edited | Abtan Massini | CC BY-SA 2.5 |
added 108 characters in body; edited title
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Aug 17, 2010 at 0:17 | history | asked | Abtan Massini | CC BY-SA 2.5 |