Subspaces of 7 x 7 skew-symmetric matrices related to the group G_2
| dc.creator | Gow, Roderick | |
| dc.date | 2008-11-08 | |
| dc.date.accessioned | 2026-07-07T10:17:05Z | |
| dc.date.available | 2026-07-07T10:17:05Z | |
| dc.description | Let $K$ be a field of characteristic different from 2 and let $C$ be an octonion algebra over $K$. We show that there is a seven-dimensional subspace of $7\times 7$ skew-symmetric matrices over $K$ which is invariant under the automorphism group of $C$. This subspace consists of elements of rank 6 when $C$ is a division algebra, and elements of rank 4 and 6 when $C$ is a split algebra. In the latter case, the automorphism group is the exceptional group $G_2(K)$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0811.1298 | |
| dc.identifier | http://arxiv.org/abs/0811.1298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173735 | |
| dc.subject | Group Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17A36 | |
| dc.title | Subspaces of 7 x 7 skew-symmetric matrices related to the group G_2 | |
| dc.type | text |