| Title:
|
Octonionic Cayley spinors and $E_6$ (English) |
| Author:
|
Dray, Tevian |
| Author:
|
Manogue, Corinne A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
193-207 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
octonions |
| Keyword:
|
$E_6$ |
| Keyword:
|
exceptional Lie groups |
| Keyword:
|
Dirac equation |
| MSC:
|
17A35 |
| MSC:
|
17C90 |
| MSC:
|
22E70 |
| idZBL:
|
Zbl 1224.17006 |
| idMR:
|
MR2682473 |
| . |
| Date available:
|
2010-05-21T12:43:13Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140099 |
| . |
| Reference:
|
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