Geodesic
Octonionic Cayley spinors and $E_6$
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 193-207

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

MR   Zbl

Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group $E_6$, and of its subgroups. We are therefore led to a description of $E_6$ in terms of $3\times 3$ octonionic matrices, generalizing previous results in the $2\times 2$ case. Our treatment naturally includes a description of several important subgroups of $E_6$, notably $G_2$, $F_4$, and (the double cover of) $SO(9,1)$. An interpretation of the actions of these groups on the squares of 3-component Cayley spinors is suggested.
Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group $E_6$, and of its subgroups. We are therefore led to a description of $E_6$ in terms of $3\times 3$ octonionic matrices, generalizing previous results in the $2\times 2$ case. Our treatment naturally includes a description of several important subgroups of $E_6$, notably $G_2$, $F_4$, and (the double cover of) $SO(9,1)$. An interpretation of the actions of these groups on the squares of 3-component Cayley spinors is suggested.
Classification : 17A35, 17C90, 22E70
Keywords: octonions; $E_6$; exceptional Lie groups; Dirac equation 
Dray, Tevian; Manogue, Corinne A. Octonionic Cayley spinors and $E_6$. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 193-207. http://geodesic.mathdoc.fr/item/CMUC_2010_51_2_a4/
@article{CMUC_2010_51_2_a4,
     author = {Dray, Tevian and Manogue, Corinne A.},
     title = {Octonionic {Cayley} spinors and $E_6$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {193--207},
     year = {2010},
     volume = {51},
     number = {2},
     mrnumber = {2682473},
     zbl = {1224.17006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2010_51_2_a4/}
}
TY  - JOUR
AU  - Dray, Tevian
AU  - Manogue, Corinne A.
TI  - Octonionic Cayley spinors and $E_6$
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2010
SP  - 193
EP  - 207
VL  - 51
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_2010_51_2_a4/
LA  - en
ID  - CMUC_2010_51_2_a4
ER  - 
%0 Journal Article
%A Dray, Tevian
%A Manogue, Corinne A.
%T Octonionic Cayley spinors and $E_6$
%J Commentationes Mathematicae Universitatis Carolinae
%D 2010
%P 193-207
%V 51
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_2010_51_2_a4/
%G en
%F CMUC_2010_51_2_a4