Fusion category explained
is
algebraically closed, then the latter is equivalent to
by
Schur's lemma.
Examples
of cardinality
over a field
is a fusion category if and only if
and the characteristic of
are coprime. This is because of the condition of semisimplicity which needs to be checked by the
Maschke's theorem.
Reconstruction
Under Tannaka–Krein duality, every fusion category arises as the representations of a weak Hopf algebra.
References
- Etingof. Pavel. Nikshych. Dmitri. Ostrik. Viktor. 2005. On Fusion Categories. Annals of Mathematics. 162. 2. 581–642. 10.4007/annals.2005.162.581 . 0003-486X.
Book: Etingof. Pavel. Nikshych. Dmitri. Ostrik. Viktor. 2005. Tensor Categories. 0885-4653.
