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

1996/12/02 by Maurice Kibler, Kibler, Maurice
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #dg-ga #math-ph #math.DG #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.dg-ga/9612002

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)

arxiv created 1996/12/02 · arxiv updated 2009/11/30

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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