New solutions to the Hurwitz problem on square identities

Abstract : The Hurwitz problem of composition of quadratic forms, or of "sum of squares identity" is tackled with the help of a particular class of $(\mathbb{Z}_2)^n$-graded non-associative algebras generalizing the octonions. This method provides an explicit formula for the classical Hurwitz-Radon identity and leads to new solutions in a neighborhood of the Hurwitz-Radon identity.
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Submitted on : Wednesday, May 9, 2012 - 11:52:49 AM
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Anna Lenzhen, Sophie Morier-Genoud, Valentin Ovsienko. New solutions to the Hurwitz problem on square identities. Journal of Pure and Applied Algebra, Elsevier, 2011, 215 (12), pp.2903-2911. ⟨10.1016/j.jpaa.2011.04.011⟩. ⟨hal-00695590⟩



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