V. Krcadinac and V. Volenec
A class of quasigroups associated with a cubic Pisot number

In this paper idempotent medial quasigroups satisfying the identity ab.a)a = b are studied. An example are the complex numbers with multiplication defined by a.b = (1-q)a+qb, where q is a solution of q³-2q²+q-1=0. The positive root of this cubic equation can be viewed as a generalization of the golden ratio. It turns out that the quasigroups under consideration have many similar properties to the so-called golden section quasigroups.