New solutions to the Hurwitz problem on square identities (1007.2337v2)

Published 14 Jul 2010 in math.AC, math.NT, and math.RA

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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