The Ring of Support-Classes of $\mathrm{SL}\_2(\mathbb{F}\_q)$

Abstract

We introduce and study a subring $\mathcal{SC}$ of $\mathbb{Z}[\mathrm{SL}\_2(\mathbb{F}\_q)]$ obtained by summing elements of $\mathrm{SL}\_2(\mathbb{F}\_q)$ according to their support. The ring $\mathcal{S}C$ can be used for the construction of several association schemes.