Matrix Representations of Octonions and Their Applications
| dc.creator | Tian, Yongge | |
| dc.date | 2000-03-26 | |
| dc.date | 2000-04-01 | |
| dc.date.accessioned | 2026-07-07T04:34:27Z | |
| dc.date.available | 2026-07-07T04:34:27Z | |
| dc.description | As is well-known, the real quaternion division algebra $ {\cal H}$ is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra ${\cal O}$ can not be algebraically isomorphic to any matrix algebras over the real number field ${\cal R}$, because ${\cal O}$ is a non-associative algebra over ${\cal R}$. However since ${\cal O}$ is an extension of ${\cal H}$ by the Cayley-Dickson process and is also finite-dimensional, some pseudo real matrix representations of octonions can still be introduced through real matrix representations of quaternions. In this paper we give a complete investigation to real matrix representations of octonions, and consider their various applications to octonions as well as matrices of octonions. | |
| dc.description | 23 pages, LaTex | |
| dc.identifier | https://arxiv.org/abs/math/0003166 | |
| dc.identifier | http://arxiv.org/abs/math/0003166 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58905 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 15A33; 15A06; 15A24; 17A35 | |
| dc.title | Matrix Representations of Octonions and Their Applications | |
| dc.type | text |