The Ring of Support-Classes of $\mathrm{S}\mathrm{L}\mathrm{\_}2(\mathbb{F}\mathrm{\_}q)$

We introduce and study a subring $\mathcal{S}\mathcal{C}$ of $\mathbb Z[$\mathrm{S}\mathrm{L}$_2(\mathbb F_q)]$obtainedbysummingelementsof$$\mathrm{S}\mathrm{L}$_2(\mathbb F_q)$accordingtotheirsupport\mathrm{.}Thering$\mathcal SC$ can be used for the construction of several association schemes.