# 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

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topDray, 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 -

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