Timeline for When are the braid relations in a quasitriangular Hopf algebra equivalent?
Current License: CC BY-SA 3.0
9 events
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| Apr 17, 2016 at 8:45 | comment | added | zibadawa timmy | @Turion A little thought and I realized we don't need to go as fancy as group doubles. Group duals suffice. I've edited that into my answer. | |
| Apr 17, 2016 at 8:44 | history | edited | zibadawa timmy | CC BY-SA 3.0 |
and dualizing gives the first but not the second
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| Apr 17, 2016 at 8:39 | history | edited | zibadawa timmy | CC BY-SA 3.0 |
an example using a dual of a group algebra (satisfies second but not first braid relation)
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| Apr 17, 2016 at 7:59 | comment | added | Manuel Bärenz | Thanks, I understood now! I'll look for an example as well. | |
| Apr 17, 2016 at 7:52 | comment | added | zibadawa timmy | @Turion An explicit example I do not know, but perhaps I can work one out in my spare time. | |
| Apr 17, 2016 at 7:47 | comment | added | zibadawa timmy | @Turion As far as a condition to guarantee the equivalence, I don't know. I doubt there is a fully general such condition, so it's reasonable to pursue specific cases of interest. As far as what I've said, the paper I pointed out should make it relatively easy (or at least plausible) to construct examples that satisfy one relation but not the other. By Radford's paper, one condition guarantees the associated morphism is an algebra map, and the other gurantees coalgebra. So construct an algebra but not coalgebra map, say, and then convert it into an element of the tensor product. | |
| Apr 17, 2016 at 7:42 | comment | added | Manuel Bärenz | I've edited my question and hopefully clarified it. | |
| Apr 17, 2016 at 7:38 | comment | added | Manuel Bärenz | I'm not exactly sure I understood you, but that's not my question. My question is, e.g.: Are there examples for elements $R \in H \otimes H$ that satisfy all axioms for a quasitriangular structure, including the first braid axiom, but excluding the second? Or, vice versa, is there an additional axiom such that every $R$ which is known to satisfy all axioms except the second braid axiom also satisfies that second braid axiom automatically (such as half-twist Hopf algebras). | |
| Apr 17, 2016 at 4:24 | history | answered | zibadawa timmy | CC BY-SA 3.0 |