On Commuting Exponentials in Low Dimensions

2005/07/21 by Bourgeois Gerald, Gerald, Bourgeois
Mathematics · #39B42 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:39B42

paper · pdf · doi:10.48550/arxiv.math/0507446

7 pages

arxiv created 2005/07/21 · arxiv updated 2009/12/01

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.

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