We found that the set of regular circulate matrices of order n is a group, giving rise to n dimensional circulate geometry. Some invariants are found. The question when Lorentz transformation are valid in it is of particular interest. We found the following facts: if n = 2 there are Lorentz transformations, if n = 4 there are double extended Lorentz transformations, if n = 6 there are triple extended Lorentz transformations, in the case n = 3 or n = 5 there are not Lorenz transformations. The problem for arbitrary n is open now.

   

Back

GEORGI NADJAKOV INSTITUTE OF SOLID STATE PHYSICS
Bulgarian Academy of Sciences
72 Tsarigradsko chaussee blvd.
BG-1784 Sofia, Bulgaria
Phone: +359 (0)2 979 58 31; GSM +359 (0)899 75 05 90
Fax: +359 (0)2 975 36 32
E-mail: gkamish@issp.bas.bg
Skype: physmuseum

Created: 18 July 2011
Updated: 21 October 2015