On Commuting Exponentials in Low Dimensions

Abstract

We introduce and study the following relation between 2 linear functions f,g on a vector space of dimension d<=3: exp(tf+g)=exp(tf)exp(g) for every t an integer. If d=2 then f,g are simultaneously trigonalizable. If d=3 the same relation holds given a supplementary condition. In this manner we can avoid the postulate 2i(Pi) congruence free which has been used by researchers since 1954.