Octonionic Cayley spinors and E 6

Tevian Dray; Corinne A. Manogue

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 2, page 193-207
  • ISSN: 0010-2628

Abstract

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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 × 3 octonionic matrices, generalizing previous results in the 2 × 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) S O ( 9 , 1 ) . An interpretation of the actions of these groups on the squares of 3-component Cayley spinors is suggested.

How to cite

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Dray, Tevian, and Manogue, Corinne A.. "Octonionic Cayley spinors and $E_6$." Commentationes Mathematicae Universitatis Carolinae 51.2 (2010): 193-207. <http://eudml.org/doc/37752>.

@article{Dray2010,
abstract = {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.},
author = {Dray, Tevian, Manogue, Corinne A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {octonions; $E_6$; exceptional Lie groups; Dirac equation; octonions; ; exceptional Lie group; Dirac equation},
language = {eng},
number = {2},
pages = {193-207},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Octonionic Cayley spinors and $E_6$},
url = {http://eudml.org/doc/37752},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Dray, Tevian
AU - Manogue, Corinne A.
TI - Octonionic Cayley spinors and $E_6$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 2
SP - 193
EP - 207
AB - 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.
LA - eng
KW - octonions; $E_6$; exceptional Lie groups; Dirac equation; octonions; ; exceptional Lie group; Dirac equation
UR - http://eudml.org/doc/37752
ER -

References

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