On quadratic and nonquadratic forms: application to R$^{2m} \rightarrow$ R$^{2m-n}$ nonbijective transformations - IN2P3 - Institut national de physique nucléaire et de physique des particules Access content directly
Conference Papers Year : 1997

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.

Dates and versions

in2p3-00005049 , version 1 (18-11-1998)

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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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