2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53431By consireding representation theory for non-associative algebras we construct the fundamental and adjoint representations of the octonion algebra. We then show how these representations by associative matrices allow a consistent octonionic gauge theory to be realised. We find that non-associativity implies the existence of new terms in the transformation laws of fields and the kinetic term of an octonionic Lagrangian.20 pages,latex, UM- P-92/60High Energy Physics - Theorytext