Cyclic group representations for relation algebras $57_{65}$ and $63_{65}$

Abstract

We exhibit finite cyclic group representations for relation algebras $57_{65}$ and $63_{65}$. As a consequence, of the ten symmetric integral RAs on four atoms having at least one flexible atom, all are now known to have a representation over a finite cyclic group except for $33_{65}$, which is not even known to be finitely representable.