| Title:
|
A symplectic representation of $E_7$ (English) |
| Author:
|
Dray, Tevian |
| Author:
|
Manogue, Corinne A. |
| Author:
|
Wilson, Robert A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
387-399 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We explicitly construct a particular real form of the Lie algebra $\mathfrak e_7$ in terms of symplectic matrices over the octonions, thus justifying the identifications $\mathfrak e_7\cong \mathfrak{sp}(6,\mathbb O)$ and, at the group level, $E_7\cong\text{Sp}(6,\mathbb O)$. Along the way, we provide a geometric description of the minimal representation of $\mathfrak e_7$ in terms of rank 3 objects called cubies. (English) |
| Keyword:
|
exceptional Lie algebras |
| Keyword:
|
octonions |
| Keyword:
|
$E_7$ |
| MSC:
|
17A35 |
| MSC:
|
17B25 |
| MSC:
|
20G41 |
| idZBL:
|
Zbl 06391549 |
| idMR:
|
MR3225616 |
| . |
| Date available:
|
2015-01-19T10:54:55Z |
| Last updated:
|
2016-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143814 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
