4 problems

A premodular category is a braided fusion category equipped with a compatible spherical, equivalently ribbon, structure. Its rank $r$ is the number of isomorphism classes of simple…

Let $\mathcal{C}$ be a premodular category, let $X_a$ be a simple object, and let $N=\operatorname{ord}(T)$, where $T$ is the twist matrix. The dimension of $X_a$ is denoted by…

Müger's conjecture. Any unitary premodular category $\mathcal{K}$ has a minimal modular extension. The conjecture seeks existence of modular extensions satisfying the stated dimens…

To any simple Lie algebra $\mathfrak{g}$ and $q\in\mathbb C$ with $q^2$ a primitive $\ell$th root of unity, let $\mathcal{C}(\mathfrak{g},q,\ell)$ be the Hermitian premodular categ…