Recall the fact that the representations of a quantum group form a braided tensor category, and this corresponds to the fact that $U_q(\mathfrak g)$ is a quasi-triangular Hopf algebra. The braiding ...
Let $V$ be a (right-)$H$ comodule wrt a coaction $\Delta_R$, where $H$ is a co-quasi-triangular Hopf algebra with co-quasi-triangular Hopf algebra structure $R$. It is well-known that $V$ has a ...
I've seen some definitions of "right partial trace" and "left partial trace" in http://arxiv.org/abs/1103.1660, but these don't seem canonical in any way. The motivation for this questions is that ...
Even with the connection to quantum groups being made clearer (I believe it was not known when the Jones polynomial was first introduced), it seems to me that still we don't have the "right" ...
A classical result of Larson and Sweedler says that a finite dimensional Hopf algebra over a field has invertible antipode. Does this result extend to the setting of Hopf algebras in braided ...
So, if you talk to the right people, they will tell you that the braiding of the category of representations of a quantum group are not unitary and that one can fix this by taking a different commutor ...