On the Drinfeld center of the Verlinde category ${\text{Ver}}_p$

We provide some information about the Drinfeld center $\mathbb{Z}({\text{Ver}}_p)$ of the Verlinde category ${\text{Ver}}_p$. We compute explicitly the Cartan matrix, bound quiver and cohomology of $\mathbb{Z}({\text{Ver}}_p^{+})$, and prove that the category $\mathcal{Z}({\text{Ver}}_p^{+})$ is wild for every $p\ge 7$. In the special case $p=5$, we show that $\mathbb{Z}({\text{Ver}}_5^{+})$ has exactly $10$ non-isomorphic indecomposable objects, classify them and describe the Green ring of $\mathbb{Z}({\text{Ver}}_5^{+})$, and compute the semisimplification of $\mathbb{Z}({\text{Ver}}_5^{+})$.