On quadratic and nonquadratic forms: Application to nonbijective R^{2m} -> R^{2m-n} transformations

Details On quadratic and nonquadratic forms: Application to nonbijective R^{2m} -> R^{2m-n} transformations On quadratic and nonquadratic forms: Application to nonbijective R^{2m} -> R^{2m-n} transformations

1996-12-02

arxiv.org/abs/dg-ga/9612002v1

Physics

Mathematical Physics

14 pages, Tex File. Work presented both to the Symposium ``Symmetries in Science IX'' (Bregenz, Austria, 6-10 August 1996) and

Scientific paper

Hurwitz 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.

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