Geodesic
The upper triangular algebra loop of degree $4$
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 4, pp. 457-470

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A natural loop structure is defined on the set $U_4$ of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A detailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group.
Classification : 20N05
Keywords: algebra group; quasigroup; loop; supercharacter; fusion scheme 
@article{CMUC_2014__55_4_a2,
     author = {Johnson, K. W. and Munywoki, M. and Smith, Jonathan D. H.},
     title = {The upper triangular algebra loop of degree $4$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {457--470},
     publisher = {mathdoc},
     volume = {55},
     number = {4},
     year = {2014},
     mrnumber = {3269008},
     zbl = {06391554},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2014__55_4_a2/}
}
TY  - JOUR
AU  - Johnson, K. W.
AU  - Munywoki, M.
AU  - Smith, Jonathan D. H.
TI  - The upper triangular algebra loop of degree $4$
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2014
SP  - 457
EP  - 470
VL  - 55
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2014__55_4_a2/
LA  - en
ID  - CMUC_2014__55_4_a2
ER  - 
%0 Journal Article
%A Johnson, K. W.
%A Munywoki, M.
%A Smith, Jonathan D. H.
%T The upper triangular algebra loop of degree $4$
%J Commentationes Mathematicae Universitatis Carolinae
%D 2014
%P 457-470
%V 55
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2014__55_4_a2/
%G en
%F CMUC_2014__55_4_a2
Johnson, K. W.; Munywoki, M.; Smith, Jonathan D. H. The upper triangular algebra loop of degree $4$. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 4, pp. 457-470. http://geodesic.mathdoc.fr/item/CMUC_2014__55_4_a2/