Partial groupoid representations and a relation with the Birget–Rhodes expansion

Abstract

We introduce partial groupoid representations of a finite groupoid $\mathcal{G}$ on an algebra $\mathcal{A}$. We also show that the partial groupoid representations of $\mathcal{G}$ are in one-to-one correspondence with the representations of the algebra generated by the Birget–Rhodes expansion ${\mathcal{G}}^{\mathrm{BR}}$ of $\mathcal{G}$.