# On quadratic and nonquadratic forms: application to R$^{2m} \rightarrow$ R$^{2m-n}$ nonbijective transformations

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.
Document type :
Conference papers

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Submitted on : Wednesday, November 18, 1998 - 3:12:35 PM
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### Citation

M. Kibler. On quadratic and nonquadratic forms: application to R$^{2m} \rightarrow$ R$^{2m-n}$ nonbijective transformations. Symposium on Symmetries in Science 9, Aug 1996, Bregenz, Austria. pp.354. ⟨in2p3-00005049⟩

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