All Questions

Kaplansky's sixth conjecture [Ka75] states that the dimension of a semisimple finite dimensional Hopf algebra over $\mathbb{C}$ is divisible by the dimension of its irreducible complex representations....

This sequel of Is there a strongly noncommutative fusion category? is motivated to know whether every fusion category is "equivalent" (in some sense) to one with a commutative Grothendieck ...

A fusion category is called noncommutative if its Grothendieck ring is noncommutative. Let us call a fusion category strongly noncommutative if every fusion category Morita equivalent to it (i.e. same ...

A fusion category is called simple if its fusion subcategories are just $Vec$ and itself. Let us call a fusion category strongly simple if every fusion category Morita equivalent to it (i.e. same ...

Let $\mathcal{C}$ be a monoidal category. There is a notion of Morita equivalence of algebra objects internal to $\mathcal{C}$. Does each Morita class have a symmetric Frobenius representative? A Hopf ...

Following the notation of Etingof-Nikshych-Ostrik what is Out(G-mod) for a finite group G? That is what are all bimodule cateogries over the fusion category G-mod of complex G-modules which have the ...