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

Maurice Kibler
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Abstract

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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BibTeXRIS

Maurice Kibler. 1996-12-02. On quadratic and nonquadratic forms: Application to nonbijective R^{2m} -> R^{2m-n} transformations. https://arxiv.org/abs/dg-ga/9612002

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