2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152189Hurwitz transformations are defined as specific automorphisms of a Cayley-Dickson algebra. These transformations generate quadratic and nonquadratic forms. We investigate here the Hurwitz transformations corresponding to Cayley-Dickson algebras of dimensions 2m = 2, 4 and 8. The Hurwitz transformations which lead to quadratic forms are discussed from geometrical and Lie-algebraic points of view. Applications to number theory and dynamical systems are briefly examined.14 pages, Tex File. Work presented both to the Symposium ``Symmetries in Science IX'' (Bregenz, Austria, 6-10 August 1996) and to the Symposium ``III Catalan Days on Applied Mathematics'' (Lleida, Spain, 27-29 November 1996)Differential GeometryMathematical PhysicsQuantum Physicstext