Matrix Representations of Octonions and Their Applications

dc.creatorTian, Yongge
dc.date2000-03-26
dc.date2000-04-01
dc.date.accessioned2026-07-07T04:34:27Z
dc.date.available2026-07-07T04:34:27Z
dc.descriptionAs 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.description23 pages, LaTex
dc.identifierhttps://arxiv.org/abs/math/0003166
dc.identifierhttp://arxiv.org/abs/math/0003166
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58905
dc.subjectRings and Algebras
dc.subject15A33; 15A06; 15A24; 17A35
dc.titleMatrix Representations of Octonions and Their Applications
dc.typetext

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