Vector Lattices on a Set of Two Generators

It is proved that the center of an automorphism group $\operatorname{Aut}(FVL2)$ of a free vector lattice $FVL2$ on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice $FVL2$ has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in $FVL2$ are amply described. Similar results are obtained for a free vector lattice $FVL_Q2$ generated by two elements over a field of rational numbers.