Timeline for 180˚ vs 360˚ Twists in String Diagrams for Ribbon Categories
Current License: CC BY-SA 2.5
3 events
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| Jun 23, 2010 at 19:38 | comment | added | Peter Tingley | I actually once started working out this story in the case of representations of quantum groups. There $V$ need not necessarily isomorphic to $V^*$, but one can define natural inner products on each irreducible $V_\lambda$. Equivalently, one has a chosen system of isomorphism of vector spaces $V_\lambda \rightarrow V_\lambda^*$ (at least up to scaling). These behave quite well with respect to the representation structure, but are not morphisms). I wanted to use this as the half-twist...but never worked out the details. I've very glad to see that other people are thinking these things through! | |
| Jun 23, 2010 at 19:30 | comment | added | Peter Tingley | Thanks, I was not aware of this work. In Noah's language, perhaps the most obvious guess for a "dark side functor" would be duality. A half twist should then be a natural transformation from the identity functor $C \rightarrow C'$ and the duality functor, and it seems Selinger is exactly writing down the conditions to make this work. | |
| Jun 23, 2010 at 17:14 | history | answered | supercooldave | CC BY-SA 2.5 |