A Groupoid Approach to Interacting Fermions

We consider the algebra $\dot\Sigma(\mathcal L)$ generated by inner-limit derivations over ${\rm GICAR}$ of a fermion gas populating an aperiodic Delone set $\mathcal L$. Under standard physical assumptions such as finite interaction range, Galilean invariance and continuity with respect to lattice, we demonstrate that image $\dot \Sigma(\mathcal through Fock representation can be completed groupoid-solvable pro-$C^\ast$-algebra. Our result is first step towards unlocking $K$-theoretic tools available for separable $C^\ast$-algebra applications in context interacting fermions.