5
$\begingroup$

Frohlich and Kerler classify categories with $SU(2)_k$ fusion rules and Kazdhan-Wenzl expand this to $SU(N)_k$ categories. In both cases, unless I am missing something, the classification are determined by the dimension of the generating object which seems to imply that there's a hidden pivotal structure lurking about.

Is this true? If so, how does the classification refine down to the fusion level?

$\endgroup$
2
$\begingroup$

The classification says that a fusion category $\mathcal{C}$ with the same fusion rules of $SU(N)_k$ is a twist of $SU(N)_k$ (the twists are determined by an $N$-th root of unity). The point is that $SU(N)_k$ is pivotal (even more is spherical), and a twist of a pivotal fusion category is again pivotal (same for spherical).

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.