On quadratic and nonquadratic forms: Application to nonbijective R^{2m} -> R^{2m-n} transformations
dg-ga
2008-02-03 v1 Mathematical Physics
Differential Geometry
math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.dg-ga/9612002,
title = {On quadratic and nonquadratic forms: Application to nonbijective R^{2m} -> R^{2m-n} transformations},
author = {Maurice Kibler},
journal= {arXiv preprint arXiv:dg-ga/9612002},
year = {2008}
}
Comments
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)