Diagonal torsion matrices associated with modular data

Modular data are commonly studied in mathematics and physics. A modular datum defines a finite-dimensional representation of the modular group $\mathrm{SL}_2(\mathbb{Z})$. Cuntz (2007) defined isomorphic integral modular data. Here we discuss isomorphic integral and non-integral modular data as well as non-isomorphic but closely related modular data. In this paper, we give some insights into diagonal torsion matrices associated to modular data.