Geodesic
On the Structure of the Schild Group in Relativity Theory
Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 774-790

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DOI

Alfred Schild has established conditions that Lorentz transformationsmap world-vectors $(ct,x,y,z)$ with integer coordinates onto vectors of the same kind. These transformations are called integral Lorentz transformations.This paper contains supplements to our earlier work with a new focus on group theory. To relate the results to the familiar matrix group nomenclature, we associate Lorentz transformations with matrices in $\text{SL}(2,\mathbb{C})$ . We consider the lattice of subgroups of the group originated in Schild's paper and obtain generating sets for the full group and its subgroups.
DOI : 10.4153/CMB-2016-084-8
Mots-clés : 22E43, 20H99, 83A05, Lorentz transformation, integer lattice, Gaussian integers, Schild group, subgroup 
Jensen, Gerd; Pommerenke, Christian. On the Structure of the Schild Group in Relativity Theory. Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 774-790. doi: 10.4153/CMB-2016-084-8
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     author = {Jensen, Gerd and Pommerenke, Christian},
     title = {On the {Structure} of the {Schild} {Group} in {Relativity} {Theory}},
     journal = {Canadian mathematical bulletin},
     pages = {774--790},
     year = {2017},
     volume = {60},
     number = {4},
     doi = {10.4153/CMB-2016-084-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-084-8/}
}
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